Re: incompleteness and inconsistency


abo wrote:
For instance, when Wiles provided his proof of FLT, there was some initial
worries by logicians whether it would go through in ZFC. But the
mathematicians did not, as I understand it, share these concerns.

That is evil and wrong, though.
Surely, in this group, even if nowhere else,
it is appropriate to ask, from JUST WHAT axioms
is FLT being alleged to follow?
It would seem to me that since the question is about
natural numbers, the first question would be NOT whether
it follows from ZFC, but rather, whether it follows from PA.
It presumably doesn't, but wouldn't actually PROVING THAT
be a newsworthy result? Wouldn't it be pretty much the
shortest and most elegant example of something independent
of PA? Or does the fact that it has unbounded exponentiation
mean that it was not in PA's language to begin with?

.

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