Timeline for Inner models and strongly compact cardinals
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 19, 2016 at 9:58 | comment | added | Mohammad Golshani | @JoelDavidHamkins Yes, it seems even this weaker version is not known. | |
| May 19, 2016 at 4:01 | comment | added | Mohammad Golshani | - and Chang's conjecture, generic elementary embeddings and inner models for huge cardinals. I may also mention the worn of Neeman and Steel ``Equiconsistencies at subcompact cardinals''. | |
| May 19, 2016 at 3:59 | comment | added | Mohammad Golshani | @AsafKaragila Let me add more such results other those mentioned by Prof. Hamkins. One is the work of Foreman on inner models for Huge cardinals. See Smoke and mirrors: combinatorial properties of small cardinals equiconsistent with huge cardinals | |
| May 18, 2016 at 11:44 | comment | added | Joel David Hamkins | Mohammad, it is a nice question. I don't think we know even how to get at least one measurable cardinal below the strongly compact cardinal in an inner model, let alone unboundedly many. | |
| May 18, 2016 at 11:26 | comment | added | Joel David Hamkins | @AsafKaragila Yes, there are some arguments producing inner models of very large cardinals. See for example my paper with Apter and Gitman: jdh.hamkins.org/innermodelswithlargecardinals. For example, if there is a supercompact cardinal, then there is an inner model with an indestructible supercompact cardinal, and another inner model with a supercompact cardinal at which the GCH fails. Our methods don't seem, however, to answer the current question. | |
| May 18, 2016 at 8:28 | comment | added | Asaf Karagila♦ | I don't know enough about inner model theory, but are there any ad hoc inner models for very large cardinals? I mean, are there even results of this type known? | |
| May 18, 2016 at 6:07 | history | asked | Mohammad Golshani | CC BY-SA 3.0 |