Finite axiomatization of $\textbf{GL}\times\textbf{S5}$ and $\textbf{Grz}\times\textbf{S5}$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912786363187200 |
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| author | Bezhanishvili, Guram Khan, Mashiath |
| author_facet | Bezhanishvili, Guram Khan, Mashiath |
| contents | We prove that $\mathbf{GL} \times \mathbf{S5}$ is product matching, and that $\mathbf{Grz} \times \mathbf{S5}$ is axiomatizable by adding to $[\mathbf{Grz},\mathbf{S5}]$ the Gödel translation of the monadic Casari formula. This settles the question of the finite axiomatizability of these logics posed by Gabbay and Shehtman (1998). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09381 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite axiomatization of $\textbf{GL}\times\textbf{S5}$ and $\textbf{Grz}\times\textbf{S5}$ Bezhanishvili, Guram Khan, Mashiath Logic 03B45, 03C90, 06E25 We prove that $\mathbf{GL} \times \mathbf{S5}$ is product matching, and that $\mathbf{Grz} \times \mathbf{S5}$ is axiomatizable by adding to $[\mathbf{Grz},\mathbf{S5}]$ the Gödel translation of the monadic Casari formula. This settles the question of the finite axiomatizability of these logics posed by Gabbay and Shehtman (1998). |
| title | Finite axiomatization of $\textbf{GL}\times\textbf{S5}$ and $\textbf{Grz}\times\textbf{S5}$ |
| topic | Logic 03B45, 03C90, 06E25 |
| url | https://arxiv.org/abs/2512.09381 |