Timeline for Are there known ways to posit definable global choice in ZF without positing V=L?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 11, 2014 at 13:52 | vote | accept | Colin McLarty | ||
| Dec 10, 2014 at 16:21 | answer | added | Ali Enayat | timeline score: 10 | |
| Dec 10, 2014 at 16:15 | comment | added | Asaf Karagila♦ | @Mohammad: To be accurate, global choice can be forced over models of $\sf NBG+AC$ without adding sets. Doing this over models of $\sf ZFC$ requires us to extend the language by adding a the generic class. Sure, this is not an actual issue, but it's more accurate this way. | |
| Dec 10, 2014 at 15:03 | comment | added | Philip Welch | @Colin : You can, consistently relative to ZF, have full GCH in HOD if you wish, or else weak failures of the kind ($\aleph_\omega$ is a strong limit) you mention. | |
| Dec 10, 2014 at 14:47 | history | edited | Colin McLarty | CC BY-SA 3.0 |
Incorporate insight from the comments.
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| Dec 10, 2014 at 14:40 | comment | added | Mohammad Golshani | You can force global choice over any model of $ZFC$ without adding any new sets. | |
| Dec 10, 2014 at 14:32 | comment | added | Ali Enayat | To follow up on Philp Welch's comment: see the following posting by Joel Hamkins: mathoverflow.net/questions/180727/… | |
| Dec 10, 2014 at 14:27 | comment | added | Philip Welch | You can always assume V=HOD (the latter the hereditarily ordinal definable sets). Indeed HOD is the largest class for which there exists a definable bijection with the class of ordinals. See for example, Drake or Jech's book. | |
| Dec 10, 2014 at 14:00 | history | asked | Colin McLarty | CC BY-SA 3.0 |