When do modal definability and preservation theorems transfer to the finite?
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915857779654656 |
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| author | van Benthem, Johan Cate, Balder ten Yang, Xi |
| author_facet | van Benthem, Johan Cate, Balder ten Yang, Xi |
| contents | We study which classic modal definability and preservation results survive when attention is restricted to finite structures, where many first-order transfer theorems are known to break down. Several semantic characterizations for modal formula classes survive the passage to the finite, while a number of first-order preservation theorems for basic frame operations fail. Our main positive result is that the Bisimulation Safety Theorem does transfer to finite structures. We also discuss computability aspects, and analogues in the finite for the Goldblatt-Thomason theorem and for modal correspondence theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12171 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | When do modal definability and preservation theorems transfer to the finite? van Benthem, Johan Cate, Balder ten Yang, Xi Logic in Computer Science We study which classic modal definability and preservation results survive when attention is restricted to finite structures, where many first-order transfer theorems are known to break down. Several semantic characterizations for modal formula classes survive the passage to the finite, while a number of first-order preservation theorems for basic frame operations fail. Our main positive result is that the Bisimulation Safety Theorem does transfer to finite structures. We also discuss computability aspects, and analogues in the finite for the Goldblatt-Thomason theorem and for modal correspondence theory. |
| title | When do modal definability and preservation theorems transfer to the finite? |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2603.12171 |