Compactness in Team Semantics

We provide two proofs of the compactness theorem for extensions of first-order logic based on team semantics. First, we build upon Lück’s ultraproduct construction for team semantics and prove a suitable version of Łoś’ 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.