On duality and model theory for polyadic spaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866917698994176000 |
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| author | van Gool, Sam Marquès, Jérémie |
| author_facet | van Gool, Sam Marquès, Jérémie |
| contents | This paper is a study of first-order coherent logic from the point of view of duality and categorical logic. We prove a duality theorem between coherent hyperdoctrines and open polyadic Priestley spaces, which we subsequently apply to prove completeness, omitting types, and Craig interpolation theorems for coherent or intuitionistic logic. Our approach emphasizes the role of interpolation and openness properties, and allows for a modular, syntax-free treatment of these model-theoretic results. As further applications of the same method, we prove completeness theorems for constant domain and Gödel-Dummett intuitionistic predicate logics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_01018 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On duality and model theory for polyadic spaces van Gool, Sam Marquès, Jérémie Logic Category Theory 03C07 (Primary), 06D50, 18C10, 18A15 (Secondary) This paper is a study of first-order coherent logic from the point of view of duality and categorical logic. We prove a duality theorem between coherent hyperdoctrines and open polyadic Priestley spaces, which we subsequently apply to prove completeness, omitting types, and Craig interpolation theorems for coherent or intuitionistic logic. Our approach emphasizes the role of interpolation and openness properties, and allows for a modular, syntax-free treatment of these model-theoretic results. As further applications of the same method, we prove completeness theorems for constant domain and Gödel-Dummett intuitionistic predicate logics. |
| title | On duality and model theory for polyadic spaces |
| topic | Logic Category Theory 03C07 (Primary), 06D50, 18C10, 18A15 (Secondary) |
| url | https://arxiv.org/abs/2210.01018 |