FOM: Two questions

[Mark Steiner]

Thanks to Charles for "clarifying" (that's a charitable way of putting
it) my question. I would ask permission to add that, though indeed the
question is whether NxFx, the cardinality operator is "core
mathematics," so that we have an example of core mathematics not
definable in ZFC, the answer to the question IMHO depends on the quality
of the reasoning (i.e. the proofs) that you can do with this operator.
Frege has an ingenious proof idea, which defines the concept "natural
number," in such a way as not to assume that each natural number has a
successor, but from which the induction principle follows; then he uses
the induction principle to prove that every number has a successor.  As
an outsider, I would not presume to give grades to mathematicians; but
this proof idea is no less interesting (to me) than the proof that each
prime number has a "succesor."  I believe that Boolos also thought so.

Thanks also to Yoav and John (Baldwin) for the interesting model
theoretic information.