Timeline for Ultrafilters preserved by $\mathbb{P}$ but not by products?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 19, 2017 at 18:24 | comment | added | Asaf Karagila♦ | @Jing: Just CH is not enough. Jensen had proved the consistency of CH with "There are no Suslin trees" (SH), so some additional assumptions are needed. | |
| Oct 14, 2016 at 21:46 | comment | added | Jing Zhang | Thanks! I think it might be a good exercise to figure this out (though I don't know how hard it is). But any sketch or pointer would be appreciated ;-) . | |
| Oct 13, 2016 at 23:05 | comment | added | Joel David Hamkins | Gunter Fuchs has told me that evidently the construction of a self-specializing Suslin tree was known before his rediscovery, so he didn't publish. But I'm not sure of a reference. Paul Larson has mentioned that it was known earlier. | |
| Oct 12, 2016 at 2:05 | comment | added | Joel David Hamkins | If you follow the link, Gunter Fuchs has a construction from $\Diamond$. I'm not sure if he ever published the argument. I recall that it was very nice. | |
| Oct 12, 2016 at 2:02 | comment | added | Jing Zhang | Also any references on how to construct such trees (assuming maybe only CH but I suspect diamond)? Thanks. | |
| Oct 12, 2016 at 1:51 | comment | added | Jing Zhang | Thanks for a nice example. I've been looking at mainly proper forcings whose product remains proper (or rather just Sacks forcing). But this example is great. | |
| Oct 12, 2016 at 1:37 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |