more from Robert S. Wolf

### Single Idea 13533

#### [catalogued under 5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models]

Full Idea

The three foundations of first-order model theory are the Completeness theorem, the Compactness theorem, and the Löwenheim-Skolem-Tarski theorem.

Gist of Idea

First-order model theory rests on completeness, compactness, and the Löwenheim-Skolem-Tarski theorem

Source

Robert S. Wolf (A Tour through Mathematical Logic [2005], 5.3)

Book Reference

Wolf,Robert S.: 'A Tour Through Mathematical Logic' [Carus Maths Monographs 2005], p.172

A Reaction

On p.180 he notes that Compactness and LST make no mention of |- and are purely semantic, where Completeness shows the equivalence of |- and |=. All three fail for second-order logic (p.223).