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Löwenheim-Skolem Theorem

A fundamental result in Model Theory which states that if a countable theory has a model, then it has a countable model. Furthermore, it has a model of every Cardinality greater than or equal to $\aleph_0$ (Aleph-0). This theorem established the existence of ``nonstandard'' models of arithmetic.

See also Aleph-0, Cardinality, Model Theory


Chang, C. C. and Keisler, H. J. Model Theory, 3rd enl. ed. New York: Elsevier, 1990.

© 1996-9 Eric W. Weisstein