Compactness in team semantics

Pub Date : 2024-05-27 DOI:10.1002/malq.202200072
Joni Puljujärvi, Davide Emilio Quadrellaro
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Abstract

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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团队语义的紧凑性
我们为基于团队语义的一阶逻辑扩展提供了两个紧凑性定理证明。首先,我们以 Lück [16] 的团队语义超积构造为基础,证明了一个合适版本的 Łoś' Theorem。其次,我们证明了通过使用合适的饱和模型,我们可以将 Kontinen 和 Yang [13] 的证明推广到具有任意多变量的公式集。
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