Sayantan Roy made a presentation on «Abstract Model Structures and Compactness Theorems»

A session of the research seminar "From the Logical Point of View" was held on November 19.

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 talk, using the notion of 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.