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An Interpretation of the Zermelo-Fraenkel Set Theory and the Kelley-Morse Set Theory in a Positive Theory

✍ Scribed by Olivier Esser

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
530 KB
Volume
43
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

An interesting positive theory is the GPK theory. The models of this theory include all hyperuniverses (see [5] for a definition of these ones). Here we add a form of the axiom of infinity and a new scheme to obtain GPK~∞~^+^. We show that in these conditions, we can interprete the Kelley‐Morse theory (KM) in GPK~∞~^+^ (Theorem 3.7). This needs a preliminary property which give an interpretation of the Zermelo‐Fraenkel set theory (ZF) in GPK~∞~^+^. We also see what happens in the original GPK theory. Before doing this, we first need to study the basic properties of the theory. This is done in the first two sections.

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## Abstract This is a study of the relative interpretability of the axiom of extensionality in the positive set theory. This work has to be considered in the line of works of R. O. Gandy, D. Scott and R. Hinnion who have studied the relative interpretability of the axiom of extensionality in set th