Timeline for Arguments against large cardinals
Current License: CC BY-SA 4.0
21 events
| when toggle format | what | by | license | comment | |
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| Aug 21 at 1:09 | answer | added | Jesse Elliott | timeline score: 1 | |
| Apr 2 at 21:26 | comment | added | Wd Fusroy | "From this point of view, it's like using the standard rationals or standard reals, rather than their non-standard counterparts." ....... That sounds interesting, but I have no idea where you are going with such an analogy. Do you mean it is possible, and desirable, to stay within SAnal if one assumes V = L? But what does that imply about NSAnal. reals etc.? Or am I reading too much, or something wrong, into your use of that analogy? NSA has many diff.s with SA., -- "esp.ly the "undenomitability" of set members -- but I don't see how that's relevant to the issue of rejecting Large Cards. | |
| Jan 8, 2019 at 8:44 | history | edited | Denis Serre | CC BY-SA 4.0 |
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| Jan 8, 2019 at 4:21 | answer | added | Dmytro Taranovsky | timeline score: 11 | |
| Dec 6, 2016 at 16:03 | answer | added | Joseph Van Name | timeline score: 4 | |
| Jul 23, 2013 at 15:33 | comment | added | Włodzimierz Holsztyński | I always had a theory roughly dual to the standard theory of sets. The dual theory would have only finite sets, it would go in the other direction. I have never spent time to develope it though. | |
| Jul 23, 2013 at 14:28 | history | protected | François G. Dorais | ||
| Dec 31, 2010 at 22:09 | history | edited | Jason |
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| Oct 30, 2010 at 15:12 | answer | added | Andreas Blass | timeline score: 40 | |
| Oct 30, 2010 at 9:31 | history | edited | user8996 | CC BY-SA 2.5 |
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| Oct 29, 2010 at 23:12 | comment | added | arsmath | Basically. There are certain sets we know how to construct, and we don't need any others to do ordinary mathematics, so let's add the axiom that says that's it. It's a natural point of view. Non-set-theorists will sometimes slip into this kind of thinking, and end up implicitly assuming the continuum hypothesis until it's pointed out to them. From this point of view, it's like using the standard rationals or standard reals, rather than their non-standard counterparts. | |
| Oct 29, 2010 at 22:00 | answer | added | Andrés E. Caicedo | timeline score: 54 | |
| Oct 29, 2010 at 20:45 | comment | added | Stefan Geschke | Hm, interesting. How would you make an affirmative case for V=L? The universe should be as small as possible? Gödel rejected V=L, if I remember correctly. Most set theorists consider L (or rather its construction) as an important technical tool but reject V=L as being too restrictive (sort of like using the rationals or algebraic numbers instead of all the reals). | |
| Oct 29, 2010 at 20:04 | answer | added | Lucas K. | timeline score: 2 | |
| Oct 29, 2010 at 16:17 | comment | added | arsmath | That's worth expanding into a proper answer, Ricky. It's not hard to make an affirmative case for V=L, even though most set theorists reject it. | |
| Oct 29, 2010 at 15:48 | answer | added | arsmath | timeline score: 7 | |
| Oct 29, 2010 at 14:57 | answer | added | Timothy Chow | timeline score: 25 | |
| Oct 29, 2010 at 10:23 | answer | added | Stefan Geschke | timeline score: 31 | |
| Oct 29, 2010 at 10:22 | answer | added | David Roberts♦ | timeline score: 16 | |
| Oct 29, 2010 at 10:15 | comment | added | user5810 | One example is that if you 'believe' V=L, that puts a limit on what large cardinals exist. | |
| Oct 29, 2010 at 9:40 | history | asked | user8996 | CC BY-SA 2.5 |