Abstract Model Structures and Compactness Theorems
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912461925384192 |
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| author | Roy, Sayantan Basu, Sankha S. Chakraborty, Mihir K. |
| author_facet | Roy, Sayantan Basu, Sankha S. Chakraborty, Mihir K. |
| contents | The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the syntactic/semantic particularities of the corresponding logic. In this paper, using the notion of \emph{abstract model structures}, we show that one can develop a generalized notion of compactness that is independent of these. Several characterization theorems for a particular class of compact abstract model structures are also proved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02343 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Abstract Model Structures and Compactness Theorems Roy, Sayantan Basu, Sankha S. Chakraborty, Mihir K. Logic 03C95, 03B22 The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the syntactic/semantic particularities of the corresponding logic. In this paper, using the notion of \emph{abstract model structures}, we show that one can develop a generalized notion of compactness that is independent of these. Several characterization theorems for a particular class of compact abstract model structures are also proved. |
| title | Abstract Model Structures and Compactness Theorems |
| topic | Logic 03C95, 03B22 |
| url | https://arxiv.org/abs/2507.02343 |