Timeline for Why should we believe in the axiom of regularity?
Current License: CC BY-SA 4.0
25 events
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| Jun 25 at 18:32 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
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| Jun 25 at 18:17 | history | edited | Martin Sleziak |
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| Apr 20, 2019 at 22:46 | review | Close votes | |||
| Apr 21, 2019 at 0:36 | |||||
| Apr 9, 2019 at 11:58 | answer | added | Rodrigo Freire | timeline score: 7 | |
| Apr 9, 2019 at 8:43 | comment | added | Andrej Bauer | @BenCrowell: coming to the party a bit late, but Barwise and Moss wrote a textbook Vicious Circles in which they show applications of non-wellfounded set theory, ranging from economics to programming languages. | |
| Apr 9, 2019 at 8:13 | history | edited | Denis Serre | CC BY-SA 4.0 |
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| Mar 2, 2016 at 21:18 | comment | added | Wojowu | @SebastianGoette That's indeed some point to consider. However, by similar reasoning, we should accept V=L as an axiom, which generally isn't done, because V=L is often considered too restrictive. One could interpret my question as asking why, on the other hand, foundation isn't considered to be too restrictive as well. | |
| Mar 2, 2016 at 16:07 | answer | added | Goldstern | timeline score: 5 | |
| Mar 2, 2016 at 4:16 | answer | added | Vladimir Reshetnikov | timeline score: 13 | |
| Oct 27, 2015 at 1:04 | comment | added | fhyve | Should this not be "how is the axiom of regularity useful"? | |
| Oct 1, 2015 at 23:20 | comment | added | user21349 | We could turn this around and ask whether there is any reason to disbelieve the axiom of regularity. A strong reason to disbelieve it would be if there were some part of mathematics (group theory, differential geometry, number theory, ...) in which we found that it was inconvenient to be restricted to the kind of sets that are well-founded. | |
| Oct 1, 2015 at 16:33 | answer | added | Flash Sheridan | timeline score: 1 | |
| Oct 1, 2015 at 8:13 | comment | added | Avshalom | @AsafKaragila But their long branches may be more visible on a sunny day. | |
| Sep 30, 2015 at 14:00 | vote | accept | Wojowu | ||
| Sep 30, 2015 at 12:26 | answer | added | anemone | timeline score: 6 | |
| Sep 30, 2015 at 11:42 | comment | added | David Roberts♦ | Nice one, @Asaf... | |
| Sep 30, 2015 at 10:56 | comment | added | Asaf Karagila♦ | @David: You can't see the forest for the trees if you look at it this way! | |
| Sep 30, 2015 at 10:14 | answer | added | Andreas Blass | timeline score: 38 | |
| Sep 30, 2015 at 7:17 | comment | added | David Roberts♦ | @AndrésCaicedo and if you come from a structural set theory background, ZFC et al is just the study of certain well-founded trees. | |
| Sep 30, 2015 at 6:35 | answer | added | Thomas Benjamin | timeline score: 4 | |
| S Sep 29, 2015 at 22:50 | history | suggested | CommunityBot | CC BY-SA 3.0 |
Fixed one typo
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| Sep 29, 2015 at 22:42 | review | Suggested edits | |||
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| Sep 29, 2015 at 19:24 | answer | added | Peter LeFanu Lumsdaine | timeline score: 63 | |
| Sep 29, 2015 at 19:02 | comment | added | Andrés E. Caicedo | I think it is in a sense just a matter of convenience. On the other hand, everything of interest has a well-founded "surrogate" (using Pen's expression), so there is no loss here (this is important, if you take seriosuly the idea of maximizing expressive power). All this said, foundation is really key to the way we deal with sets nowadays. Adrian Mathias once went so far as to say that modern set theory is really the study of well-foundedness. | |
| Sep 29, 2015 at 18:31 | history | asked | Wojowu | CC BY-SA 3.0 |