more from Wilfrid Hodges

### Single Idea 10287

#### [catalogued under 5. Theory of Logic / K. Features of Logics / 6. Compactness]

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.

Gist of Idea

If a first-order theory entails a sentence, there is a finite subset of the theory which entails it

Source

Wilfrid Hodges (First-Order Logic [2001], 1.10)

Book Reference

'Blackwell Guide to Philosophical Logic', ed/tr. Goble,Lou [Blackwell 2001], p.29

A Reaction

If entailment is possible, it can be done finitely.