Tarski Formalization Project Archives
The posted input files are now all mechanically generated from a master list of theorems.
For more information about our methodology see the top page of this project.
Chapter 12 is about parallel lines. We follow the suggestion of SST, since we are working with points and not sets, and take 12.7 as the definition of parallel, rather than 12.2. Specifically, $Line(p,q)$ is parallel to $Line(a,b)$ if they do not meet, and $p$ and $q$ are on the same side of $Line(a,b)$. This definition works without any dimension axiom,
because Tarski's definition of "same side" works without a dimension axiom.
The key theorem in the chapter is Satz 12.11, which is Hilbert's
parallel axiom, namely, given line $L$ and point $a$ not on $L$, there is at most one line through $a$
parallel to $L$. The proof begins by assuming there are two such lines, $B$ and $C$.
The first claim in the book proof of Satz 12.11 (just below the diagram) is the
existence of the point $c^\prime$, which is insufficiently justified by "da <$B$ und $C$ sich in $a$ schneiden"
("because $B$ and $C$ meet in $a$"). (This is one of only two insufficiently justified claims that we found in the text we formalized; the other was Satz 11.49.) We call this claim Lemma 12.11 and prove it in two separate files, because we could not manage to get Otter to combine the cases that arise. The second of those files in turn
depends on Lemma 9.13f, a version of the plane separation theorem that does not occur in SST. That
lemma depends on the dimension axiom for dimension two. Since our aim was to do plane geometry, we were
content with that result. It looks quite a bit more complicated to fix Szmielew's proof in $n$ dimensions.
The lines $B$ and $C$ have to be specified by two points in Tarski's theory, and
it is not fair to assume those points are the ones shown in the diagram; so there are four extra points
not shown in the diagram, and even getting a contradiction from the assumption $a=d$ is
not trivial using Otter, though it seems apparent from the diagram. We had to prove Satz 12.11 in two
cases, according as $a=d$ or $a\neq d$. The supposedly trivial case takes 55 steps. We were
not able to combine these cases into a single proof, even with the aid of the tautology $a=d \lor a \neq d$. Of course we
could just derive it from the two cases, but the case distinction is on whether two constructed points
coincide or not, so the cases would have to be formulated more generally, and there seems little point.
The times shown in the following table are not the times required to find the proof, but rather
the maximum time allocated to Otter to find the proof. The time is shown only when it had to be longer than
the default, which was often 20 seconds when hints were used and 120 seconds when hints were not used.
The posted input files are now all mechanically generated from a master list of theorems.
The times shown in the following table are not the times required to find the proof, but rather
the maximum time allocated to Otter to find the proof. The time is shown only when it had to be longer than
the default, which was often 20 seconds when hints were used and 120 seconds when hints were not used.
For more information about our methodology see the top page of this project.
| Input File |
Proof |
Length |
Strategy |
Seconds |
Commentary |
#!/usr/bin/php
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168
Deprecated: strstr(): Passing null to parameter #1 ($haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185
Back to top of archive
