Timeline for Reference request: forcing diamond at every stationary subset of every regular cardinal
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 13, 2021 at 2:30 | comment | added | Jason Zesheng Chen | while this isn't quite what you're looking for, you might be interested to take a look at the appendix of Large cardinals need not be large in HOD and the references there to the works of Friedman and Brooke-Taylor on coding into the diamond pattern. | |
| Mar 7, 2021 at 2:05 | comment | added | Asaf Karagila♦ | "Like the fella once said, ain't that a kick in the head?" | |
| Mar 7, 2021 at 0:19 | comment | added | Sean Cox | @AsafKaragila that would definitely prevent what I'm trying to do! | |
| Mar 6, 2021 at 21:57 | comment | added | Asaf Karagila♦ | Assume no inaccessible cardinals exist. Problem solved. | |
| Mar 6, 2021 at 19:22 | comment | added | Sean Cox | Thanks. Diamond easily holds at successor cardinals after Jensen's forcing, but it's not obvious that it holds at inaccessibles. A math fairy sent me an email with some abstract reasons this should be true for those type of iterations, but I'd prefer a more explicit adding of diamonds everywhere (i.e. at all regulars). I think I'll just write a very brief appendix on it. | |
| Mar 6, 2021 at 18:59 | comment | added | Todd Eisworth | Maybe more helpful: The construction of forcing GCH using class forcing is due to Jensen, in an abstract of the Notices that doesn't appear in Mathscinet. See Exercise 15.15 in Jech's 3rd Millenium edition and references at end of his chapter. If you can find a reference for why the collapses he uses force diamond, you're done. | |
| Mar 6, 2021 at 18:55 | comment | added | Sean Cox | I guess I can also just put in into a short appendix, so people who don't want to think about forcing iterations can happily never encounter it... | |
| Mar 6, 2021 at 18:54 | comment | added | Sean Cox | @ToddEisworth ha ha, yes that does answer the question as posed, but I really need it to be an Easton support iteration (so that I can cite another black box about progressively closed Easton support iterations). | |
| Mar 6, 2021 at 18:33 | comment | added | Todd Eisworth | Overkill, but can't you use Jensen coding to extend to a model L[x] for x a real? That's probably citable... ;) | |
| Mar 6, 2021 at 15:25 | history | asked | Sean Cox | CC BY-SA 4.0 |