Löwenheim-Skolem theorem

Etymology
Named for Leopold Löwenheim and Thoralf Skolem.

Proper noun

 * 1)  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.