Timeline for What is the definition of a large cardinal axiom?
Current License: CC BY-SA 3.0
22 events
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| Feb 16, 2022 at 12:09 | answer | added | Binary198 | timeline score: -1 | |
| Feb 2, 2014 at 1:11 | answer | added | Everett Piper | timeline score: 6 | |
| Jan 24, 2014 at 20:18 | answer | added | Joseph Van Name | timeline score: 3 | |
| Jan 24, 2014 at 18:31 | comment | added | Joel David Hamkins | Timothy, I agree with that, but I think the actual project here is to poke holes in the all the proposed answers. | |
| Jan 24, 2014 at 17:56 | comment | added | user45939 | @EverettPiper: Thanks. Would you please add a link for the paper? | |
| Jan 24, 2014 at 17:15 | history | edited | user45939 |
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| Jan 24, 2014 at 15:40 | comment | added | Timothy Chow | I confess that I'll be disappointed (!) if this question has a good answer. I believe that there are certain mathematical concepts that derive their utility from not being formal, and "large cardinal axiom" is, IMO, one of them. Another example is the term "sieve" in number theory. It's so ingrained in most of us that formalizing a definition constitutes "progress" that I think it's good to have a few clear counterexamples lying around. | |
| Jan 24, 2014 at 14:57 | answer | added | Mohammad Golshani | timeline score: 10 | |
| Jan 24, 2014 at 14:46 | comment | added | Asaf Karagila♦ | Sort of like mathoverflow.net/questions/104016/… | |
| Jan 24, 2014 at 14:32 | comment | added | Joel David Hamkins | And just to clarify, of course we are not looking for examples of large cardinal axioms, but rather a formal definition of what it means for an axiom to be a large cardinal axiom. This is a fairly slippery concept, and naive attempts to formalize this are typically inadequate. | |
| Jan 24, 2014 at 13:59 | history | reopened |
Joel David Hamkins Daniel Moskovich Chris Godsil François G. Dorais |
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| Jan 24, 2014 at 13:37 | comment | added | Joel David Hamkins | I would be interested to learn what are the various technical definitions that have been proposed, such as the one mentioned by Everett, and I consider this question on-topic for MO. | |
| Jan 24, 2014 at 7:19 | review | Reopen votes | |||
| Jan 24, 2014 at 14:01 | |||||
| Jan 24, 2014 at 5:50 | comment | added | Everett Piper | @StevenLandsburg: Couldn't it move toward a consensus? Sites like this provide a deeper and at the same time broader understanding of topics informed by experts working in the field, even if that understanding borders on what might be considered more philosophical concerns. If the only "definitions" of large cardinal are implicitly understood, so be it. But certainly we could benefit from having a single source collecting together some of these implicit "definitions", right? | |
| Jan 24, 2014 at 5:41 | comment | added | Steven Landsburg | @EverettPiper: If there is no consensus on the topic, then the question has no answer and probably doesn't belong here. | |
| Jan 24, 2014 at 5:16 | comment | added | Everett Piper | I think this is actually an important, if soft, question worthy of discussion by set-theorists with some interest in the subject. There is at least one formal definition that I know of offered by Woodin in part II of his article on CH in the AMS. I don't know if he himself considers the definition there satisfactory, but there doesn't seem to be any consensus on the topic (as far as I can tell). | |
| Jan 24, 2014 at 5:10 | history | closed |
Andrés E. Caicedo David Roberts♦ S. Carnahan♦ |
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| Jan 24, 2014 at 5:08 | comment | added | David Roberts♦ | I suggest asking this on math.stackexchange.com if this question is closed. | |
| Jan 24, 2014 at 5:03 | review | Close votes | |||
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| S Jan 24, 2014 at 4:48 | review | Low quality posts | |||
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| S Jan 24, 2014 at 4:48 | review | First posts | |||
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| Jan 24, 2014 at 4:29 | history | asked | user45939 | CC BY-SA 3.0 |