Timeline for Is it consistent with ZFC(A) for the Hartogs number of a proper class to be $\aleph_0$?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 8, 2023 at 17:57 | vote | accept | NoLongerBreathedIn | ||
| May 8, 2023 at 4:06 | comment | added | Bokai Yao | @Holo I'd like to add that permutation is not needed for getting a proper class with Hartogs number $\aleph_0$. Taking sets with finite kernels will do. | |
| May 6, 2023 at 20:08 | comment | added | Holo | For another possible reference, following Jech's book "the axiom of choice" in chapter 9 problem 3 and 4 they construct models of ZFCA with infinitely many atoms but every set contains only finitely many atoms in its transitive closure by generalizing permutation models whose permutations are permutations over a proper class, in such models the Hartogs number of the class of atoms is $\aleph_0$ | |
| May 4, 2023 at 19:25 | comment | added | NoLongerBreathedIn | @AlecRhea Does that include proper classes definable from set parameters? | |
| May 4, 2023 at 19:24 | comment | added | NoLongerBreathedIn | @JamesHanson Yep | |
| May 4, 2023 at 4:42 | comment | added | Asaf Karagila♦ | math.stackexchange.com/a/1619246/622 | |
| May 4, 2023 at 3:55 | answer | added | Bokai Yao | timeline score: 10 | |
| May 4, 2023 at 2:27 | comment | added | Alec Rhea | Conservativity of GBC over ZFC specifically refers to statements about sets -- GBC can prove things about proper classes that ZFC can't, so your last sentence seems dubious to me. | |
| May 3, 2023 at 23:25 | comment | added | James E Hanson | Are you talking about a version of ZFCA where the collection of atoms do not need to form a set? | |
| S May 3, 2023 at 23:10 | review | First questions | |||
| May 4, 2023 at 0:43 | |||||
| S May 3, 2023 at 23:10 | history | asked | NoLongerBreathedIn | CC BY-SA 4.0 |