Combining Philosophers

Ideas for Hermarchus, Wilfrid Hodges and John Charvet

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1 idea

5. Theory of Logic / K. Features of Logics / 6. Compactness

10287	If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W]
	Full Idea: Compactness Theorem: suppose T is a first-order theory, ψ is a first-order sentence, and T entails ψ. Then there is a finite subset U of T such that U entails ψ.
	From: Wilfrid Hodges (First-Order Logic [2001], 1.10)
	A reaction: If entailment is possible, it can be done finitely.