Tennenbaum's theorem is a result in mathematical logic, specifically in the field of model theory. It states that there is no non-standard model of Peano arithmetic (PA) that satisfies the conditions of being both a model of PA and having a linear ordering of its elements that corresponds to the standard ordering of the natural numbers.
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Tennenbaum's theorem says that no countable nonstandard model of Peano arithmetic can have both addition and multiplication computable under a presentation of its domain by the natural numbers.