Recursive Structures For PA
A structure in the language of PA is recursive if there are recursive functions + and × from to, a recursive two-place relation < on, and distinguished constants such that
where indicates isomorphism and is the set of (standard) natural numbers. Because the isomorphism must be a bijection, every recursive model is countable. There are many nonisomorphic countable nonstandard models of PA.
Read more about this topic: Tennenbaum's Theorem
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