Abstract Model Structures and Compactness Theorems

Sayantan Roy; Sankha S. Basu; Mihir K. Chakraborty

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arXiv · 2507.02343

Abstract Model Structures and Compactness Theorems

Sayantan Roy·Sankha S. Basu·Mihir K. Chakraborty

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Abstract

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.

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BibTeX RIS

Sayantan Roy, Sankha S. Basu, Mihir K. Chakraborty. 2025-07-03. Abstract Model Structures and Compactness Theorems. https://arxiv.org/abs/2507.02343

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