# syntactic compactness theorem for first order logic

Let $L$ be a first-order language, and $\Delta\subseteq L$ be a set of sentences. If $\Delta$ is inconsistent, then some finite $\Gamma\subseteq\Delta$ is inconsistent.

Title syntactic compactness theorem for first order logic SyntacticCompactnessTheoremForFirstOrderLogic 2013-03-22 12:43:59 2013-03-22 12:43:59 jihemme (316) jihemme (316) 5 jihemme (316) Theorem msc 03B10 msc 03C07 UpwardsSkolemLowenheimTheorem ProofOfUpwardsSkolemLowenheimTheorem GettingModelsIModelsConstructedFromConstants