[FOM] Logical Status of FLT
Harvey Friedman
friedman at math.ohio-state.edu
Wed Oct 6 00:15:20 EDT 2010
From the recent FOM postings on the logical status of FLT, and from
McLarty's http://www.cwru.edu/artsci/phil/Proving_FLT.pdf, I think we
can draw a few conclusions.
1. Wiles' proof of FLT is not given outright within ZFC, in the usual
sense.
2. No new ideas are needed to cast Wiles' proof in ZFC. However, there
is still a perceived need for documenting a form of Wiles' proof in ZFC.
3. Kisin's new proof of FLT is given outright within ZFC, in the usual
sense.
My questions are:
4. Are new ideas needed to cast Wiles' proof in ZC? In Z_8? In Z_3? In
Z_2? In Pi11-CA_0? In ATR_0? In PA? In EFA?
5. Are new ideas needed to cast Kisin's new proof in ZC? In Z_8? In
Z_3? In Z_2? In Pi11-CA_0? In ATR_0? In PA? In EFA?
I would also like to raise the same questions with regard to Falting's
and other proofs of the Mordell Conjecture.
Harvey Friedman
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