# Michael Beeson's Research

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## Tarski Formalization Project Archives

### Chapter 8: Right angles and perpendiculars

The three main results in this chapter are all due to Gupta (1965): the existence of dropped and erected perpendiculars, in Satz 8.18 and Satz 8.22, and the application of those results to the construction of a midpoint of any segment in Satz 8.22.

These proofs by Gupta make no use of any form of the continuity axiom (in particular no circles are involved), and they also make no use of the parallel axiom, i.e., they use only neutral geometry; and they do not use the upper dimension axiom either. The proofs rely on Gupta's work in Chapter 7, specifically the fact that the base of an isosceles triangle has a midpoint and the Krippenlemma.

In these theorems, \$R(a,b,c)\$ means that \$abc\$ is a right angle, but the definition allows the "degenerate" cases in which some of all of the points are collinear or even coincide. By contrast, those cases are not allowed in the relations \$ ab \perp cd \$ or \$ perpAt(a,b,x,c,d)\$, which means that \$ab\$ and \$cd\$ are perpendicular at \$x\$.

\$s(a,p)\$ is the reflection of \$p\$ in the point \$a\$, not to be confused with the reflection of a point in a line, which cannot be introduced until after the theory of perpendiculars is developed. By \$(abc)\cong(def)\$ Tarski means that corresponding sides of the two "triangles" are congruent, even if the points are collinear or equal. The predicate \$M(a,m,b)\$ means that \$am = mb\$; \$m\$ then turns out to be unique and is called \$midpoint(a,b)\$.

The book's proof of Satz 8.22 (existence of a midpoint) proceeds by first proving what we call Satz 8.22b (without giving it a separate statment). Then the book says, "by the symmetry of the hypotheses" we can assume \$ap \le qb\$. We handle this by making 8.22b a separate theorem, which we then apply twice to prove 8.22, with different instantiations.

The last theorem in the chapter, Satz 8.24, is a more detailed statement about the midpoint, which actually gives a term to construct the midpoint, in terms of the perpendiculars. It is worth noting, however, that since the perpendiculars might be dropped or erected, SST does not give a single term that always constructs the midpoint. In addition there is another case distinction in the proof of that theorem, about which of two segments is the shorter. By "symmetry" it suffices "without loss of generality" to prove just one case, according to the book, and that is what we do in Satz 8.24a and Satz 8.24b. (Since 8.24 has a conclusion that is a conjunction, it has to become two files in resolution form.)

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.

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Input File Proof Length Strategy Seconds Commentary