[FOM] FLT and ZFC, again

Harvey Friedman friedman at math.ohio-state.edu
Thu Dec 6 12:45:00 EST 2007

On 12/6/07 11:23 AM, "Timothy Y. Chow" <tchow at alum.mit.edu> wrote:

> I recently had an email exchange with a number theorist (who prefers to
> remain anonymous, but who gave permission for his anonymized remarks to
> be forwarded to FOM) regarding the possibility that the current proof of
> Fermat's Last Theorem might require axioms beyond ZFC.  His response:
>> Oh, come on! :-) Just because a proof uses a cohomology theory doesn't
>> mean that it depends on Grothendieck universes. ...

All of this was well known to me, having talked to number theorists.

But the real issues remain: can be avoid 3rd order arithmetic? 2nd order
arithmetic? Is it provable in first order arithmetic? It is provable in
primitive recursive arithmetic? Is it provable in EFA = exponential function
arithmetic = ISigma0(exp)?

I have not worked on these problems, but have spent a fair amount of time
trying to get others to work on them.

Also, Colin McLarty had "agreed" to document the removal of Grothendieck
universes from FLT. Colin?

Harvey Friedman

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