Timeline for Bijection of proper classes
Current License: CC BY-SA 3.0
11 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| May 30, 2012 at 12:43 | comment | added | Zhen Lin | @Martin: You need to be careful when defining categories using logical formulae. Here, you should quotient out by "provable extensional equality" in order to get identity morphisms and associativity of composition. (See, for example, Part D of Sketches of an Elephant.) | |
| Jun 19, 2011 at 9:54 | comment | added | Martin Brandenburg | I used ZFC above. But GBC is perhaps better to work with classes. | |
| Jun 19, 2011 at 0:56 | comment | added | Joel David Hamkins | Martin, the treatment of classes in Goedel-Bernays set theory is not so tied to first-order definability and allows one to consider classes that are not definable by a formula. But nevertheless GBC is equiconsistent and in fact conservative over ZFC. This situation often arises in class forcing over a model of ZFC, for example, if you want the generic filter as a class, since in most cases it is not definable. | |
| Jun 18, 2011 at 10:18 | comment | added | Chris Eagle | How does this prove $\kappa^2=\kappa$ for every $\kappa \ge \aleph_0$? It seems to only work for alephs. | |
| Jun 16, 2011 at 8:27 | comment | added | Martin Brandenburg | @John: Perhaps we should allow parameters. | |
| Jun 15, 2011 at 11:06 | comment | added | John Bentin | @Martin: I don't think that the OP is positing infinite formulas. But only countably many of the maps from $\omega$ to $\omega$ (for example) are defined by formulas. | |
| Jun 14, 2011 at 21:56 | comment | added | Martin Brandenburg | How do you define infinite formulas? | |
| Jun 14, 2011 at 21:17 | comment | added | porton | I don't like defining a map as a formula. This suppresses maps which are not expressible as a finite formula. Well, in my particular case I can deal with this special case when we consider only maps expressible with a finite formula, because in my example I can write explicit formulas down. But I just don't like it. | |
| Jun 14, 2011 at 18:25 | history | edited | Martin Brandenburg | CC BY-SA 3.0 |
added 324 characters in body; added 3 characters in body
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| Jun 14, 2011 at 18:15 | history | answered | Martin Brandenburg | CC BY-SA 3.0 |