n. (Logic) the crucial result in model theory that if a countable theory has a model it has a countable model, and indeed a model of every cardinality greater than or equal to ℵ₀. For example, it shows that there exist non-standard models of arithmetic: since the theory is countable, by the Löwenheim-Skolem theorem, it has an uncountable model, which is clearly non-standard. Compare compactness theorem.