# Michael Beeson's Research

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## Tarski Formalization Project Archives

The posted input files are now all mechanically generated from a master list of theorems. For more information about our methodology see the top page of this project.

### Congruence of right triangles; triangle construction and uniqueness

The most important theorem in this chapter is Satz 10.12, which says that two right triangles with pairwise congruent legs also have congruent hypotenuses.

This is not an immediate consequence of the 5-segment axiom; the 5-segment axiom together with this theorem implies SAS, but the 5-segment axiom alone does not immediately imply SAS.

Euclid took it as a postulate that all right angles are congruent, which is essentially the content of Satz 10.12, although angle congruence is not defined until Chapter 11.

Satz 10.12 is proved in three stages: first we reduce to the case where the two triangles have their right-angled vertex in common (by reflection in the midpoint of the line joining those vertices). Then we reduce to the case where they have one leg in common. To that we need a "rotation". Rotation through a given angle can be done by reflecting in the bisector of that angle. Since we can find the midpoint of a line, by Gupta's midpoint construction, we can bisect an angle. So, the chapter begins with the definition and properties of reflection in a line. The only difficult property is that reflection preserves betweenness (Satz 10.10).

Once Satz 10.12 is in hand, and Gupta's dropped perpendiculars are available, it is an easy matter to verify Hilbert's axiom about triangle construction and uniqueness (Satz 10.16a and Satz 10.16b).

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 2168

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2171
error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2153

Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2166

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Deprecated: strstr(): Passing null to parameter #1 (\$haystack) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2168

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error in get_chapter()
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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

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error in get_chapter()
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error in get_chapter()
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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

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error in get_chapter()
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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

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error in get_chapter()
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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

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error in get_chapter()
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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

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error in get_chapter()
Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

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Deprecated: strcmp(): Passing null to parameter #1 (\$string1) of type string is deprecated in /usr/home/beeson/public_html/michaelbeeson/research/FormalTarski/TarskiTheorems.php on line 2185

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Input File Proof Length Strategy Seconds Commentary