Compactness in Team Semantics

TL;DR

This paper proves the compactness theorem for team semantics extensions of first-order logic using ultraproducts and saturated models, advancing the understanding of logical properties in this framework.

Contribution

It introduces two novel proofs of compactness for team semantics, expanding the theoretical foundations of this logical extension.

Findings

Proof using ultraproducts and { extlnot}o{\textperiodcentered}o{\textperiodcentered} theorem

Generalization to models with arbitrarily many variables

Enhanced understanding of compactness in team semantics

Abstract

We provide two proofs of the compactness theorem for extensions of first-order logic based on team semantics. First, we build upon L\"uck's ultraproduct construction for team semantics and prove a suitable version of {\L}o\'s' Theorem. Second, we show that by working with suitably saturated models, we can generalize the proof of Kontinen and Yang to sets of formulas with arbitrarily many variables.