### Single Idea 10288

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

Full Idea

Downward Löwenheim-Skolem (the weakest form): If L is a first-order language with at most countably many formulas, and T is a consistent theory in L. Then T has a model with at most countably many elements.

Gist of Idea

Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model

Source

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

Book Reference

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