The Mostowski Bridge

Ali Enayat

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arXiv · 2505.23998

The Mostowski Bridge

Ali Enayat

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Abstract

In 1950, Novak and Mostowski showed that GB (G\"odel-Bernays theory of classes) is conservative over ZF, and therefore by G\"odel's second incompleteness theorem the consistency of ZF is unprovable in GB. In the same year Mostowski unveiled a contrasting result: GB provides a truth-definition for ZF-formulae. Here we first give an expository account of Mostowski's construction and surrounding results, and then we show that the construction bridges the domain of Tarski-style truth theories over PA with certain subsystems of second order arithmetic.

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Ali Enayat. 2025-05-29. The Mostowski Bridge. https://arxiv.org/abs/2505.23998

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