I think whether naturals plus one non-standard integer line is a model of Peano’s axioms for the successor only (no addition/multiplication) depends on whether we use second order or first order logic to express induction. (No in second order formulation due to Dedekind’s result, yes for any first order formulation).
I think whether naturals plus one non-standard integer line is a model of Peano’s axioms for the successor only (no addition/multiplication) depends on whether we use second order or first order logic to express induction. (No in second order formulation due to Dedekind’s result, yes for any first order formulation).