# Michael Beeson's Research

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## Tarski Formalization Project Archives

### Chapter 9: Sides of a line, and outer Pasch from inner Pasch.

There are two major results in this chapter: the opposite-sides theorem (related to the idea that a line divides a plane into two regions), and the fact that inner Pasch implies outer Pasch. Both these results, like the main results of Chapters 7 and 8, are due to Gupta (1965).

Hilbert and Tarski agree that "p and q are on the opposite side of Line(a,b)" means that there is a point on the line strictly between p and q.

Tarski defined "p and q are on the same side of line L" to mean that there is some point c such that both segments pc and qc meet line L, and none of p,q,c lie on L. Hilbert just said it meant that pq does not meet L. Tarski's definition has the advantage of working in n-space. It also allows "plane" to be a defined concept: Three non-collinear points a,b,c determine the plane consisting of all points that are on the same side of Line(a,b) as c, or on the opposite side. But then, are the points on same side as c all on the opposite side from any one point on the opposite side? Yes, they are, according to Satz 9.8, and moreover, being on the same side of a given line is a transitive relation (Satz 9.13).

These results assert the existence of certain intersection points of lines, and hence they are intimately bound up with Pasch's axiom, which is the fundamental principle that a line entering a triangle (in the same plane as the triangle) must also exit the triangle. There are two forms of Pasch's axiom that are considered in Tarski's geometry: inner Pasch, and outer Pasch. (See my paper "A constructive version of Tarski's geometry" for diagrams.)

Both are good choices for an axiom, since their logical form is simple and they do not rely on an upper dimension axiom to be true, i.e. they are true in n-space as well as in the plane. Tarski originally took outer Pasch as an axiom, since it was known that outer Pasch implies inner Pasch. Gupta showed that inner Pasch implies outer Pasch, which is Satz 9.6. After that, Szmielew took inner Pasch as an axiom (as is done in SST), although Tarski argued in a famous letter that the development might be easier with outer Pasch as an axiom.

The theorem that inner Pasch implies outer Pasch rests on the opposite-side theorem Satz 9.5; its fairly short proof uses nothing else from Chapters 7,8, or 9. Once both forms of Pasch are available, the derivation of the properties of "sameside" is not difficult.

The opposite-side theorem (Satz 9.5) rests on what SST calls Lemma 9.4. That "Lemma" gave Otter a lot of trouble, so much that we upgraded it from "Lemma" to "Satz". We had to break it into three cases and prove them separately, and then derive Satz 9.4 from the three separately-proved cases, and even that was not trivial.

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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Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
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Input File Proof Length Strategy Seconds Commentary