Inmodel theory, a discipline withinmathematical logic, anon-standard model is a model of a theory that is notisomorphic to theintended model (or standard model).[1]
If the intended model is infinite and the language isfirst-order, then theLöwenheim–Skolem theorems guarantee the existence of non-standard models. The non-standard models can be chosen aselementary extensions orelementary substructures of the intended model.
Non-standard models are studied inset theory,non-standard analysis andnon-standard models of arithmetic.
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