{{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<!--this should not be a link to model, which is a huge disambiguation page--> of a theory that is not isomorphic to the intended model (or standard model).<ref>Roman Kossak, 2004 ''Nonstandard Models of Arithmetic and Set Theory'' American Mathematical Soc.</ref>
==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== *Interpretation (logic)
==References== {{Reflist}}
{{Mathematical logic}} {{mathlogic-stub}} {{DEFAULTSORT:Non-Standard Model}} Category:Model theory