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.

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Meanings

proper noun
  1. mathematical logicA 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

Named for Leopold Löwenheim and Thoralf Skolem.

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Cite this entry
APA

Löwenheim-Skolem theorem. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/L%C3%B6wenheim-Skolem%20theorem

MLA

“Löwenheim-Skolem theorem.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/L%C3%B6wenheim-Skolem%20theorem. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Löwenheim-Skolem theorem,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/L%C3%B6wenheim-Skolem%20theorem.

Source: Löwenheim-Skolem theorem on Wiktionary, CC BY-SA 4.0.