The Mostowski Bridge
Logic
2025-12-30 v6
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.
Cite
@article{arxiv.2505.23998,
title = {The Mostowski Bridge},
author = {Ali Enayat},
journal= {arXiv preprint arXiv:2505.23998},
year = {2025}
}
Comments
16 pages; in this version the second sentence in Remark 3.5 of the previous version has been excised due to being incorrect. A significant footnote has also been added on p.7