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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.20178 |
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| _version_ | 1866912171703664640 |
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| author | Chen, Zhicheng Ding, Yifeng |
| author_facet | Chen, Zhicheng Ding, Yifeng |
| contents | Let $n$-Medvedev's logic $\mathbf{ML}_n$ be the intuitionistic logic of Medvedev frames based on the non-empty subsets of a set of size $n$, which we call $n$-Medvedev frames. While these are tabular logics, after characterizing $n$-Medvedev frames using the property of having at least $n$ maximal points, we offer a uniform axiomatization of them through a Gabbay-style rule corresponding to this property. Further properties including compactness, disjunction property, and structural completeness of $\mathbf{ML}_n$ are explored and compared to those of Medvedev's logic $\mathbf{ML}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20178 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Logics of Individual Medvedev Frames Chen, Zhicheng Ding, Yifeng Logic Let $n$-Medvedev's logic $\mathbf{ML}_n$ be the intuitionistic logic of Medvedev frames based on the non-empty subsets of a set of size $n$, which we call $n$-Medvedev frames. While these are tabular logics, after characterizing $n$-Medvedev frames using the property of having at least $n$ maximal points, we offer a uniform axiomatization of them through a Gabbay-style rule corresponding to this property. Further properties including compactness, disjunction property, and structural completeness of $\mathbf{ML}_n$ are explored and compared to those of Medvedev's logic $\mathbf{ML}$. |
| title | The Logics of Individual Medvedev Frames |
| topic | Logic |
| url | https://arxiv.org/abs/2412.20178 |