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Wikipedia

Non-standard model

January 01, 1970

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).[1]

Existence edit

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.

Importance edit

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

See also edit

References edit

  1. ^ Roman Kossak, 2004 Nonstandard Models of Arithmetic and Set Theory American Mathematical Soc.

January 01, 1970
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