We provide two proofs of the compactness theorem for extensions of first-order logic based on team semantics. First, we build upon L & uuml;ck's [16] ultraproduct construction for team semantics and prove a suitable version of & Lstrok;o & sacute;' Theorem. Second, we show that by working with suitably saturated models, we can generalize the proof of Kontinen and Yang [13] to sets of formulas with arbitrarily many variables.
Compactness in team semantics
Quadrellaro, Davide Emilio
2024-01-01
Abstract
We provide two proofs of the compactness theorem for extensions of first-order logic based on team semantics. First, we build upon L & uuml;ck's [16] ultraproduct construction for team semantics and prove a suitable version of & Lstrok;o & sacute;' Theorem. Second, we show that by working with suitably saturated models, we can generalize the proof of Kontinen and Yang [13] to sets of formulas with arbitrarily many variables.
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