Failure of the Blok-Esakia Theorem in the monadic setting
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913600366444544 |
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| author | Bezhanishvili, Guram Carai, Luca |
| author_facet | Bezhanishvili, Guram Carai, Luca |
| contents | The Blok-Esakia Theorem establishes that the lattice of superintuitionistic logics is isomorphic to the lattice of extensions of Grzegorczyk's logic. We prove that the Blok-Esakia isomorphism $σ$ does not extend to the fragments of the corresponding predicate logics of already one fixed variable. In other words, we prove that $σ$ is no longer an isomorphism from the lattice of extensions of the monadic intuitionistic logic to the lattice of extensions of the monadic Grzegorczyk logic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09401 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Failure of the Blok-Esakia Theorem in the monadic setting Bezhanishvili, Guram Carai, Luca Logic 03B45, 03B55, 06D20, 06E25, 06E15 The Blok-Esakia Theorem establishes that the lattice of superintuitionistic logics is isomorphic to the lattice of extensions of Grzegorczyk's logic. We prove that the Blok-Esakia isomorphism $σ$ does not extend to the fragments of the corresponding predicate logics of already one fixed variable. In other words, we prove that $σ$ is no longer an isomorphism from the lattice of extensions of the monadic intuitionistic logic to the lattice of extensions of the monadic Grzegorczyk logic. |
| title | Failure of the Blok-Esakia Theorem in the monadic setting |
| topic | Logic 03B45, 03B55, 06D20, 06E25, 06E15 |
| url | https://arxiv.org/abs/2405.09401 |