Suppose you have a candidate structure, and you want to prove it satisfies the Peano axioms. For example, let 1 serve as the first element, and let $s(x)=x/(1+x)$. It's easy to see the non-induction axioms are satisfied, but how would one show the induction axiom (2nd order) or axiom schema (1st order) is satisfied?
2026-03-25 12:16:30.1774440990
How to prove Peano induction axiom for a candidate model
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