In mathematical logic, a non-standard model of arithmetic is a model of (first-order) Peano arithmetic that contains non-standard numbers. The standard model of arithmetic consists of the set of 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).
Read more about Non-standard Model Of Arithmetic: Existence, Structure of Countable Non-standard Models, References
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