Timeline for The meaning and purpose of "canonical''
Current License: CC BY-SA 4.0
29 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 27, 2020 at 21:45 | comment | added | LSpice | @AsafKaragila, that is the canonical conclusion to such questions. | |
| Feb 27, 2020 at 20:05 | answer | added | anon | timeline score: 2 | |
| Feb 25, 2020 at 20:01 | answer | added | Kevin Buzzard | timeline score: 9 | |
| Feb 23, 2020 at 1:45 | review | Close votes | |||
| Feb 23, 2020 at 20:05 | |||||
| Feb 22, 2020 at 19:54 | answer | added | abx | timeline score: 9 | |
| Feb 21, 2020 at 14:47 | answer | added | Jonny Evans | timeline score: 2 | |
| Feb 21, 2020 at 11:42 | comment | added | Asaf Karagila♦ | Looking at the answers, I wonder if maybe there is no canonical meaning to the word canonical. | |
| Feb 21, 2020 at 10:34 | comment | added | David Roberts♦ | Should this have the tag [big-list]? | |
| Feb 21, 2020 at 10:24 | answer | added | Thomas Klimpel | timeline score: 4 | |
| Feb 20, 2020 at 19:59 | comment | added | nomen | Good question. I had a professor make me pin down what I meant by a canonical object one time when I was a junior. It was a worthwhile exercise. | |
| Feb 20, 2020 at 7:34 | answer | added | Martin Brandenburg | timeline score: 12 | |
| Feb 20, 2020 at 0:06 | history | became hot network question | |||
| Feb 20, 2020 at 0:01 | answer | added | Robbie Lyman | timeline score: 4 | |
| Feb 19, 2020 at 23:34 | answer | added | Francois Ziegler | timeline score: 8 | |
| Feb 19, 2020 at 22:19 | answer | added | Rasmus Erlemann | timeline score: 2 | |
| Feb 19, 2020 at 21:45 | answer | added | Timothy Chow | timeline score: 13 | |
| Feb 19, 2020 at 20:44 | comment | added | David Corfield | "...to pick out objects with certain properties that are canonical in the sense that they are unique up to isomorphism," better to say "unique up to unique isomorphism". | |
| Feb 19, 2020 at 17:17 | comment | added | user44143 | There are also canonical examples (the theory of real-closed fields is a canonical example of quantifier elimination; the algebraic numbers are a canonical example of a real-closed field) and canonical sources (baby Rudin is a canonical text for introduction to analysis). And the canonical models you are after may be akin to the canonical stories of Star Wars. | |
| Feb 19, 2020 at 16:53 | comment | added | Asaf Karagila♦ | First you ask for canonicity. Then you'll ask for canonical canonicity. Then you'll ask about canonicity of canonicity and for a canonical canonicity of canonicity. Where will it end??? | |
| Feb 19, 2020 at 16:47 | comment | added | Monroe Eskew | @AndrésE.Caicedo Thanks for pointing out the error. I am not proposing a definition but just pointing out that the way in which things can be canonical seems to get weaker as you move to larger cardinals. So I'm trying to see if there is a solid notion underneath that accords with broader mathematical practice, which could clarify the goals of the "inner model program." | |
| Feb 19, 2020 at 16:43 | history | edited | Monroe Eskew | CC BY-SA 4.0 |
edited body
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| Feb 19, 2020 at 16:14 | comment | added | Andrés E. Caicedo | It seems you are not using an appropriate definition of canonicity in set theory. I even mentioned that in the linked question! (By the way, the link does not work.) | |
| Feb 19, 2020 at 15:28 | comment | added | Neil Barton | It's therefore a real mathematical problem to isolate what we mean in certain contexts by canonical; that's how you know when you've solved the problem. | |
| Feb 19, 2020 at 15:27 | comment | added | Neil Barton | I echo the helpfulness comment! That material is super-useful. I think especially interesting is the conjecture that it might help direct research goals. For instance, one of the key research goals in set theory is to build a canonical model for a supercompact cardinal. It's important that such a model have some sort of canonicity properties (good reasons to think that supercompacts are consistent and so there should be some model just don't satisfy the same goal). But it's very unclear what that is meant to mean given that such a beast wouldn't be unique. | |
| Feb 19, 2020 at 12:49 | comment | added | Monroe Eskew | @FrancoisZiegler Thanks for the link, it is very helpful. However I don't think it addresses the "purpose" part of our question, that is part (b). We want more than a survey of how people generally use the word; we want moreover to know what the "right" answer is based on the underlying motivations. | |
| Feb 19, 2020 at 11:53 | history | edited | Monroe Eskew | CC BY-SA 4.0 |
added 148 characters in body; edited title
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| Feb 19, 2020 at 11:20 | review | Close votes | |||
| Feb 19, 2020 at 22:35 | |||||
| Feb 19, 2020 at 11:01 | comment | added | Francois Ziegler | Does this answer your question? What is the definition of "canonical"? | |
| Feb 19, 2020 at 10:59 | history | asked | Monroe Eskew | CC BY-SA 4.0 |