non-standard model
{{Short description|Model in mathematical logic not isomorphic to the standard model}}
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).Roman Kossak, 2004 Nonstandard Models of Arithmetic and Set Theory American Mathematical Soc.
Existence
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
Non-standard models are studied in set theory, non-standard analysis and non-standard models of arithmetic.
See also
References
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{{Mathematical logic}}
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