syntactic compactness theorem for first order logicCompactnessTheoremForFirstOrderLogic2002-06-04 14:33:142002-06-09 18:03:23Theorem% this is the default PlanetMath preamble. as your knowledge
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\end{array}\right)}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.