The Mostowski Bridge
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911340256296960 |
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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 |