Timeline for Are classes still "larger" than sets without the axiom of choice?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| May 1, 2018 at 21:52 | comment | added | Elliot Glazer | You might find it interesting that the axiom in your second question requires Foundation in its prove (as well as AC, of course). I believe this axiom is called the injection principle. | |
| May 1, 2018 at 14:51 | comment | added | Gérard Lang | We can obtain a model with at least four non-equivalent proper classes On, V, A and B such that there is no injection of A into B and no injection of B into A (see"More on bijective-equivalent classes in NBG set theory (1) and (2) | |
| May 1, 2018 at 14:48 | comment | added | Gérard Lang | It is interesting to know that if we extend the notion of cardinality to proper classes (see "Order in bijective equivalent collections of proper classes in set theory"), we find that even in NBG with choice, we do not obtain a well-order at all, because in fact we do not have a total order. | |
| Apr 30, 2018 at 23:29 | vote | accept | Mike Battaglia | ||
| Apr 30, 2018 at 23:08 | history | edited | Mike Battaglia | CC BY-SA 3.0 |
edited title; edited title
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| Apr 30, 2018 at 23:02 | answer | added | Joel David Hamkins | timeline score: 26 | |
| Apr 30, 2018 at 22:52 | history | asked | Mike Battaglia | CC BY-SA 3.0 |