Single Idea 17878

[catalogued under 5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems]

Full Idea

Löwenheim's theorem reads as follows: If a first-order proposition is satisfied in any domain at all, it is already satisfied in a denumerably infinite domain.

Gist of Idea

If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain


Thoralf Skolem (Remarks on axiomatised set theory [1922], p.293)

Book Reference

'From Frege to Gödel 1879-1931', ed/tr. Heijenoort,Jean van [Harvard 1967], p.293