Compactness in Team Semantics
Joni Puljuj\"arvi, Davide Emilio Quadrellaro

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.
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Taxonomy
TopicsSemantic Web and Ontologies · Logic, Reasoning, and Knowledge · Advanced Database Systems and Queries
