Variations on a Visserian Theme

Ali Enayat

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arXiv · 1702.07093

Variations on a Visserian Theme

Ali Enayat

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Abstract

A first order theory T is said to be "tight" if for any two deductively closed extensions U and V of T (both of which are formulated in the language of T), U and V are bi-interpretable iff U = V. By a theorem of Visser, PA (Peano Arithmetic) is tight. Here we show that Z_2 (second order arithmetic), ZF (Zermelo-Fraenkel set theory), and KM (Kelley-Morse theory of classes) are also tight theories.

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Ali Enayat. 2017-02-23. Variations on a Visserian Theme. https://arxiv.org/abs/1702.07093

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