Failure of Esakia's theorem in the monadic setting
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908695748673536 |
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| author | Bezhanishvili, Guram Carai, Luca |
| author_facet | Bezhanishvili, Guram Carai, Luca |
| contents | Esakia's theorem states that Grzegorczyk's logic is the greatest modal companion of intuitionistic propositional calculus. We prove that already the one-variable fragment of intuitionistic predicate calculus does not have a greatest modal companion, yielding that Esakia's theorem fails in the monadic setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05607 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Failure of Esakia's theorem in the monadic setting Bezhanishvili, Guram Carai, Luca Logic 03B20, 03B45, 03B55 Esakia's theorem states that Grzegorczyk's logic is the greatest modal companion of intuitionistic propositional calculus. We prove that already the one-variable fragment of intuitionistic predicate calculus does not have a greatest modal companion, yielding that Esakia's theorem fails in the monadic setting. |
| title | Failure of Esakia's theorem in the monadic setting |
| topic | Logic 03B20, 03B45, 03B55 |
| url | https://arxiv.org/abs/2409.05607 |