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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
Source
Thoralf Skolem (Remarks on axiomatised set theory [1922], p.293)
Book Ref
'From Frege to Gödel 1879-1931', ed/tr. Heijenoort,Jean van [Harvard 1967], p.293
17878 | If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem] |
17879 | Axiomatising set theory makes it all relative [Skolem] |
17880 | Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem] |
17881 | Mathematician want performable operations, not propositions about objects [Skolem] |