Single Idea 10590

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

Full Idea

Upward Löwenheim-Skolem: if a set of first-order formulas is satisfied by a domain of at least the natural numbers, then it is satisfied by a model of at least some infinite cardinal.

Gist of Idea

Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them

Source

Stewart Shapiro (Higher-Order Logic [2001], 2.1)

Book Reference

'Blackwell Guide to Philosophical Logic', ed/tr. Goble,Lou [Blackwell 2001], p.34

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