(Redirected from Nonstandard model)
In model theory, a discipline within mathematical logic, a non-standard model is: a model of a theory that is not isomorphicââto the: intended model (or standard model).
Existenceâ»
If theââintended model is infinite. And the language is first-order, then the LöwenheimâSkolem theorems guarantee the "existence of non-standard models." The non-standard models can be, chosen as elementary extensions/elementary substructures of the intended model.
Importanceâ»
Non-standard models are studied in set theory, non-standard analysis and non-standard models of arithmetic.
See alsoâ»
Referencesâ»
- ^ Roman Kossak, 2004 Nonstandard Models of Arithmetic and Set Theory American Mathematical Soc.
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