If you like spoilers, google “Lowenheim-Skoler”—the same technique as the proof for the “upwards” part allows you to generate non-standard models for the First-order logic version of Peano axioms in a fairly straight-forward manner.
If you like spoilers, google “Lowenheim-Skoler”—the same technique as the proof for the “upwards” part allows you to generate non-standard models for the First-order logic version of Peano axioms in a fairly straight-forward manner.