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Non-standard model

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This is an old revision of this page, as edited by CBM (talk | contribs) at 12:04, 20 March 2011 (Undid revision 419749393 by 184.1.9.237 (talk) - this article is on mathematical logic, not particle physics). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.
See also Interpretation (logic)

In model theory, a discipline within mathematical logic, a non-standard model is a model of a theory that is not isomorphic to the intended model (or standard model). If the intended model is infinite and the language is first-order, then the Löwenheim-Skolem theorems guarantee the existence of non-standard models. The non-standard models can be chosen as elementary extensions or elementary substructures of the intended model.

Non-standard models are studied in set theory, non-standard analysis, and non-standard model of arithmetic.

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