Abstract Model Structures and Compactness Theorems
Logic
2025-07-04 v1
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.
Cite
@article{arxiv.2507.02343,
title = {Abstract Model Structures and Compactness Theorems},
author = {Sayantan Roy and Sankha S. Basu and Mihir K. Chakraborty},
journal= {arXiv preprint arXiv:2507.02343},
year = {2025}
}
Comments
33 pages. The final version of this article has been submitted for publication