If you have time for another question, I'm still confused about how it applies to second-order arithmetic, though, since the Peano axioms are well-known and easily listed on a single piece of paper. What difficulty is there be in determining whether a statement is a second-order Peano axiom?
It seems particularly strange since there are apparently fewer axioms than in first-order Peano arithmetic (by replacing an axiom schema with a single induction axiom).
If you have time for another question, I'm still confused about how it applies to second-order arithmetic, though, since the Peano axioms are well-known and easily listed on a single piece of paper. What difficulty is there be in determining whether a statement is a second-order Peano axiom?
It seems particularly strange since there are apparently fewer axioms than in first-order Peano arithmetic (by replacing an axiom schema with a single induction axiom).
[1] https://math.stackexchange.com/questions/106635/why-does-the...