We provide two proofs of the compactness theorem for extensions of first‐order logic based on team semantics. First, we build upon Lück's [16] 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 [13] to sets of formulas with arbitrarily many variables.
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Puljujärvi et al. (2024) studied this question.