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Aug
22 |
awarded | Good Answer |
Jun
25 |
awarded | Yearling |
Jul
24 |
answered | Not especially famous, long-open problems which anyone can understand |
Mar
21 |
comment |
Inaccessible cardinals and Andrew Wiles's proof
I heard Angus Macintyre talk about it fairly recently. The situation is a little unusual, as to write out a proof fully would entail multiplying the (already considerable) length of Wiles' proof by 5 (or 10 or something), to reduce every single step to PA. Macintyre does not intend to do this in full completeness, but he is continuing to prepare a manuscript to show that the key pieces of higher order machinery used in the Wiles' proof can be translated into PA. The focus is on the central modularity theorem, which he will show is effectively $\Pi^0_1$, and provable in PA. |
Aug
17 |
awarded | Supporter |
Aug
17 |
comment |
Inaccessible cardinals and Andrew Wiles's proof
Ok! Try again... Macintyre has reportedly announced a proof (which I would expect to be non-trivial) that Wiles' proof can be translated into PA. In the intro to his forthcoming book, Boolean Relation Theory and Incompleteneess, Harvey Friedman conjectures that it should be proveable in an elementary fragment $I \Sigma_0(exp)$. This is an instance of his conjecture that "Every theorem published in the Annals of Mathematics whose statement involves only finitary mathematical objects (i.e., what logicians call an arithmetical statement) can be proved in elementary arithmetic." |
Aug
17 |
awarded | Nice Answer |
Aug
16 |
comment |
Inaccessible cardinals and Andrew Wiles's proof
I now seem to have magically acquired enough reputation to comment... Very recently I have read that Angus Macintyre has announced a proof of FLT in PA. The only reference I can provide is this: cameroncounts.wordpress.com/2010/01/07/mathematics-and-logic-2 |
Aug
16 |
awarded | Teacher |
Aug
16 |
answered | Inaccessible cardinals and Andrew Wiles's proof |