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### Single Idea 10160

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

Full Idea

The Löwenheim-Skolem Theorem, the earliest in model theory, states that if a countable set of sentences in a first-order language has a model, then it has a countable model.

Gist of Idea

Löwenheim-Skolem says if the sentences are countable, so is the model

Source

Feferman / Feferman (Alfred Tarski: life and logic [2004], Int V)

Book Reference

Feferman,S/Feferman,A.B.: 'Alfred Tarski: life and logic' [CUP 2008], p.281

A Reaction

There are 'upward' (sentences-to-model) and 'downward' (model-to-sentences) versions of the theory.