Löwenheim?Skolem theorem

In mathematical logic, the classic Löwenheim?Skolem theorem states that any infinite model M has a countably infinite submodel N that satisfies exactly the same set of first-order sentences that M satisfies. A model, in this context, consists of an underlying set (often also denoted) "M", a set of relations on this set M, and a set of functions (sometimes taking several arguments) from M into itself. The theorem is named for Leopold Löwenheim and Thoralf Skolem.

Related Topics:
Mathematical logic - Model - Submodel - First-order - Leopold Löwenheim - Thoralf Skolem

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