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Non-standard model of arithmetic
In mathematical logic, a non-standard model of arithmetic is a model of (first-order) Peano arithmetic that contains non-standard numbers. The term standard model of arithmetic refers to the standard natural numbers 0, 1, 2, …. The elements of any model of Peano arithmetic are linearly ordered and possess an initial segment isomorphic to the standard natural numbers. A non-standard model is one that has additional elements outside this initial segment. The construction of such models is due to Thoralf Skolem (1934).
== Existence ==
There are several methods that can be used to prove the existence of non-standard models of arithmetic.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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