Lower order axioms

[martdowd at aol.com]

FOM
Anton Freund writes

Transfinite induction can
probably count as a natural axiom, but it is not quite as close to
mathematical practice. I would be very interested in further examples as
well.
Regarding transfinite induction relevant to arithmetic,
  https://math.stackexchange.com/questions/305288/how-to-derive-church-kleene-ordinalhas some material of interest.  Section 11 of http://dx.doi.org/10.12732/ijpam.v93i5.7might also be of interest.

Martin Dowd

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