Löwenheim-Skolem theorem (English, name)
expansion: Löwenheim-Skolem theorem
Senses:
qualifier: mathematical logic
glosses: A theorem stating that, if a countable first-order theory has an infinite model, then for every infinite cardinal number κ it has a model of size κ. The result implies that first-order theories are unable to control the cardinality of their infinite models, and that no first-order theory with an infinite model can have a unique model up to isomorphism.
Forms: