Timeline for Cardinalities larger than the continuum in areas besides set theory
Current License: CC BY-SA 2.5
25 events
| when toggle format | what | by | license | comment | |
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| Oct 20, 2021 at 11:38 | history | edited | Gerry Myerson |
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| Aug 7, 2013 at 21:28 | answer | added | Tomasz Kania | timeline score: 1 | |
| Mar 10, 2011 at 2:36 | answer | added | Justin Moore | timeline score: 10 | |
| Nov 11, 2010 at 2:59 | comment | added | Martin Brandenburg | Related question: mathoverflow.net/questions/35408/… | |
| Nov 5, 2010 at 11:23 | vote | accept | Daniel Miller | ||
| Nov 4, 2010 at 15:01 | comment | added | Andrés E. Caicedo | @Kevin: I figured; on abstract grounds, many of the uses had to be non-essential. But, as Carl Mummert pointed out, that is not necessarily the point. | |
| Nov 4, 2010 at 12:59 | comment | added | Carl Mummert | @Kevin Buzzard: I haven't seen the email, but in general, it's often possible to avoid a complex construction by talking around it. For example, we could skip all abstract group theory and only work with groups of permutations. For a more historical example, I read once that topologists understood the concept of homology groups long before they began using that terminology in papers. In principle we still "could" avoid homology groups for many results by talking around them. My personal opinion is that ''if'' something is commonly used, that's all that matters - not whether it "must" be used. | |
| Nov 4, 2010 at 11:03 | comment | added | Kevin Buzzard | BCnrd points out to me in an email that, whilst what I say is true (Aut(C) is used), it is not logically essential to use it (i.e. he knows how to prove many if not all of the results where it's used, without using it). | |
| Nov 4, 2010 at 2:49 | answer | added | Carl Mummert | timeline score: 3 | |
| Nov 4, 2010 at 2:07 | answer | added | Orr Shalit | timeline score: 5 | |
| Nov 4, 2010 at 1:03 | answer | added | Joel David Hamkins | timeline score: 35 | |
| Nov 4, 2010 at 0:28 | answer | added | Charles Staats | timeline score: 7 | |
| Nov 3, 2010 at 23:12 | answer | added | Paul Marcelo | timeline score: 2 | |
| Nov 3, 2010 at 21:47 | answer | added | Georges Elencwajg | timeline score: 73 | |
| Nov 3, 2010 at 20:38 | comment | added | Kevin Buzzard | @Andres: the automorphism group of the complex numbers is used as a tool in the theory of canonical models of Shimura varieties. Even though I can only think of two explicit automorphisms, the full group is needed. | |
| Nov 3, 2010 at 20:38 | answer | added | Stefan Geschke | timeline score: 8 | |
| Nov 3, 2010 at 19:09 | comment | added | Willie Wong | Given the title of this question, isn't it an oxymoron to tag this question "set-theory"? | |
| Nov 3, 2010 at 18:20 | history | edited | François G. Dorais |
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| Nov 3, 2010 at 18:18 | answer | added | Nate Eldredge | timeline score: 14 | |
| Nov 3, 2010 at 18:18 | answer | added | Terry Tao | timeline score: 29 | |
| Nov 3, 2010 at 18:03 | answer | added | François G. Dorais | timeline score: 9 | |
| Nov 3, 2010 at 17:48 | answer | added | Rachid Atmai | timeline score: 10 | |
| Nov 3, 2010 at 17:44 | comment | added | Andrés E. Caicedo | @Evan On the other hand, there are only 2 continuous (or even "reasonably definable") such automorphisms. | |
| Nov 3, 2010 at 17:35 | comment | added | Evan Jenkins | One famous folklore example is the automorphism group of the field of complex numbers, which has cardinality $2^{2^{\aleph_0}}$. | |
| Nov 3, 2010 at 17:27 | history | asked | Daniel Miller | CC BY-SA 2.5 |