Löwenheim-Skolem theorem
Löwenheim-Skolem theorem proper noun: 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.
Proper noun
Löwenheim-Skolem theorem
- 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.
Origin of Löwenheim-Skolem theorem
Named for Leopold Löwenheim and Thoralf Skolem.
Questions about Löwenheim-Skolem theorem
- What does Löwenheim-Skolem theorem mean?
- Löwenheim-Skolem theorem means 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.
- What part of speech is Löwenheim-Skolem theorem?
- Löwenheim-Skolem theorem is a proper noun.
Words near Löwenheim-Skolem theorem in the dictionary
Source and license
Adapted from Wiktionary: Löwenheim-Skolem theorem (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
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