Implicative models of set theory
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916122995982336 |
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| author | Maschio, Samuele Miquel, Alexandre |
| author_facet | Maschio, Samuele Miquel, Alexandre |
| contents | In this paper we show that using implicative algebras one can produce models of set theory generalizing Heyting/Boolean-valued models and realizability models of (I)ZF, both in intuitionistic and classical logic. This has as consequence that any topos which is obtained from a Set-based tripos as the result of the tripos-to-topos construction hosts a model of intuitionistic or classical set theory, provided a large enough strongly inaccessible cardinal exists. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_10576 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Implicative models of set theory Maschio, Samuele Miquel, Alexandre Logic in Computer Science Logic 03B40, 03C62 In this paper we show that using implicative algebras one can produce models of set theory generalizing Heyting/Boolean-valued models and realizability models of (I)ZF, both in intuitionistic and classical logic. This has as consequence that any topos which is obtained from a Set-based tripos as the result of the tripos-to-topos construction hosts a model of intuitionistic or classical set theory, provided a large enough strongly inaccessible cardinal exists. |
| title | Implicative models of set theory |
| topic | Logic in Computer Science Logic 03B40, 03C62 |
| url | https://arxiv.org/abs/2310.10576 |