It is in fact provably impossible to construct a computable nonstandard model (where, say, S and +, or S and × are both computable relations) in a standard model of computation.
Would you give a reference? I found it easy to find assertions such as “the completeness theorem is not constructively provable,” but this statement is a little stronger.
Would you give a reference? I found it easy to find assertions such as “the completeness theorem is not constructively provable,” but this statement is a little stronger.
Tennenbaum’s Theorem