The Mostowski Bridge

Fuente: arXiv
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Autore principale: Enayat, Ali
Natura: Preprint
Pubblicazione: 2025
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author Enayat, Ali
author_facet Enayat, Ali
contents In 1950, Novak and Mostowski showed that GB (Gödel-Bernays theory of classes) is conservative over ZF, and therefore by Gödel'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.
format Preprint
id arxiv_https___arxiv_org_abs_2505_23998
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The Mostowski Bridge
Enayat, Ali
Logic
03F35
In 1950, Novak and Mostowski showed that GB (Gödel-Bernays theory of classes) is conservative over ZF, and therefore by Gödel'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.
title The Mostowski Bridge
topic Logic
03F35
url https://arxiv.org/abs/2505.23998