Single Idea 18109

[catalogued under 5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic]

Full Idea

From the fact that the usual rules for first-level logic are complete (as proved by Gödel 1930), it follows that this logic is 'compact'.

Gist of Idea

The completeness of first-order logic implies its compactness

Source

David Bostock (Philosophy of Mathematics [2009], 5.5)

Book Reference

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.153


A Reaction

The point is that the completeness requires finite proofs.

Related Idea

Idea 10974 Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read]