Timeline for Inaccessible cardinals and Andrew Wiles's proof
Current License: CC BY-SA 4.0
22 events
| when toggle format | what | by | license | comment | |
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| May 22 at 16:51 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https
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| Jun 18, 2021 at 13:34 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
Formatting
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| Aug 19, 2011 at 1:37 | answer | added | David Roberts♦ | timeline score: 19 | |
| Aug 17, 2010 at 12:14 | comment | added | BCnrd | Dear Pierre: No. Universes have as much relevance to proof of FLT as general theory of derived categories does to finite-dim'l linear alg (i.e., no relevance). Just because certain theories (derived categories, topoi, etc.) are documented in one reference in hyper-general form using concept X doesn't imply that applications of those theories logically depend on X: there may be other ways to develop the theory (with a bit less generality), even documented in the literature, which suffice for applications of interest. Everything on this page is like a fog as far as proof of FLT is concerned. | |
| Aug 17, 2010 at 8:50 | vote | accept | Cosmonut | ||
| Aug 17, 2010 at 8:45 | vote | accept | Cosmonut | ||
| Aug 17, 2010 at 8:50 | |||||
| Aug 17, 2010 at 6:51 | comment | added | Pierre-Yves Gaillard | Dear BCnrd: Thanks a lot for your answer! Is proving FLT without universes a little bit like proving the PNT without complex analysis? | |
| Aug 17, 2010 at 5:43 | comment | added | BCnrd | Dear Pierre: if one wants to write a treatise on a general theory of cohomology on all topoi, including operations like sheafification, enough injectives, derived categories, and Ext-sheaves, there needs to be a way to control the "size" of coverings which arise in these constructions (to replace the implicit role of "power set" for ordinary topology spaces). The universe stuff takes care of such matters in an elegant way, so one can focus attention on the more central aspects of the theory. | |
| Aug 17, 2010 at 5:18 | comment | added | Pierre-Yves Gaillard | Why did Grothendieck introduce his Universes Axiom? | |
| Aug 16, 2010 at 22:25 | comment | added | Yemon Choi | I am a bit puzzled why this has now accumulated 2 votes to close (since I can't see the reasons selected by those who voted). | |
| Aug 16, 2010 at 20:55 | answer | added | Richard Elwes | timeline score: 35 | |
| Aug 16, 2010 at 18:48 | comment | added | JS Milne | The Stack Project develops a huge amount of Grothendieck style mathematics, including a lot of etale cohomology, using only ZFC (specifically, NOT using universes). If anyone has any doubt that this can be done, I suggest that they look at it. | |
| Aug 16, 2010 at 15:24 | answer | added | Noah Snyder | timeline score: 62 | |
| Aug 16, 2010 at 13:42 | answer | added | Richard Borcherds | timeline score: 30 | |
| Aug 16, 2010 at 13:41 | comment | added | JS Milne | Actually, Cosmonut misquoted the article by leaving out the rest of the statement: "But there is a general consensus among mathematicians that this was just a convenient short cut rather than a logical necessity. With a little work, Wiles's proof should be translatable into Peano arithmetic or some slight extension of it." | |
| Aug 16, 2010 at 11:56 | vote | accept | Cosmonut | ||
| Aug 17, 2010 at 8:45 | |||||
| Aug 16, 2010 at 11:41 | comment | added | BCnrd | Dear Joel: Nope. | |
| Aug 16, 2010 at 11:23 | answer | added | Pete L. Clark | timeline score: 90 | |
| Aug 16, 2010 at 11:20 | comment | added | Joel David Hamkins | Does any part of Wiles' proof or general results he may rely on make use of Grothendieck universes? The existence of these is equivalent to the existence of an inaccessible cardinal. | |
| Aug 16, 2010 at 11:13 | comment | added | Robin Chapman | Wiles's paper jstor.org/stable/2118559 makes no mention of inacessible cardinals. | |
| Aug 16, 2010 at 11:12 | comment | added | BCnrd | No, completely false. Perhaps the author (whose mathematical training seems to be far from number theory) has misunderstood or misheard descriptions of parts of the argument. | |
| Aug 16, 2010 at 10:41 | history | asked | Cosmonut | CC BY-SA 2.5 |