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Model theory is the branch of mathematical logic which deals with the connection between a formal language and its interpretations, or models.

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Do bijections from the natural numbers satisfy the Peano axioms? [closed]

While thinking of natural numbers as anything that satisfies the Peano axioms, I was left wondering, what if I take the successor function $S(x)$ to be anything other than $x\to x+1$? Some examples we …