Timeline for Cardinality of classes
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 7 at 16:41 | comment | added | Hypnosifl | In these theories is there no equivalent to a power set, a "power class" for any given proper class? Or is there such a thing as a power class, but unlike in set theory it's not true that the cardinality of a power class is larger than the original class? | |
| Aug 21, 2023 at 12:24 | review | Suggested edits | |||
| Aug 21, 2023 at 16:03 | |||||
| Mar 30, 2013 at 16:26 | comment | added | Wolphram jonny | Do this "largest" cardinal have a name? | |
| Mar 30, 2013 at 16:24 | comment | added | Wolphram jonny | But, if we extend the definition of cardinal to bijections among elements of two entities (not necessarily sets, but also proper classes), why can't we define the cardinality of the proper class of the set of all sets? It would be useful in the sense that now you do have the largest possible cardinal number (it would not be inconsistent with cantor's theorem because the proper class in not a set so there is not such thing a the power set of a class). Why is this not useful? | |
| Mar 8, 2012 at 14:54 | comment | added | Andrés E. Caicedo | Just to drive the point home, if choice fails, it may not be possible to force it back. For example, one cannot force (local) choice over Gitik's model where all (well-ordered) cardinals have cofinality $\omega$. | |
| Mar 8, 2012 at 14:20 | comment | added | Andreas Blass | Yes, one can force global choice. Andres's assertion that this won't add sets and is therefore conservative over set theory presupposes, of course, local choice in the set theory. | |
| Mar 8, 2012 at 8:37 | comment | added | Asaf Karagila♦ | So one can simply force global choice? | |
| Oct 31, 2010 at 13:46 | vote | accept | CommunityBot | moved from User.Id=10290 by developer User.Id=35285 | |
| Oct 31, 2010 at 4:24 | history | answered | Andrés E. Caicedo | CC BY-SA 2.5 |