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Single Idea 17929

[from 'Introduction to the Philosophy of Mathematics' by Mark Colyvan, in 5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems ]

Full Idea

Löwenheim proved that if a first-order sentence has a model at all, it has a countable model. ...Skolem generalised this result to systems of first-order sentences.

Gist of Idea

Löwenheim proved his result for a first-order sentence, and Skolem generalised it

Source

Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 2.1.2)

Book Reference

Colyvan,Mark: 'An Introduction to the Philosophy of Mathematics' [CUP 2012], p.25