Timeline for Large cardinal axioms and the perfect set property
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 23, 2011 at 4:07 | vote | accept | Rachid Atmai | ||
| Oct 23, 2011 at 4:02 | comment | added | François G. Dorais | @alephomega: The only way I know to prove PSP for large subscripts is using determinacy and the unfolding trick. Unfolding immediately gives the next $\Sigma$ pointclass up the ladder. I have no idea how you could avoid the extra step and just have PSP for $\Pi$ pointclass and not the next $\Sigma$ pointclass. | |
| Oct 23, 2011 at 3:58 | comment | added | François G. Dorais | Todd, I don't think so but I must admit I suffer from the same type of nearsightedness you do. There is a great paper by Brendle and Löwe that has a bunch of these characterizations; I don't think they do large subscripts, but that's where I'd check first. | |
| Oct 23, 2011 at 3:47 | comment | added | Rachid Atmai | @Todd: That's what I was asking about. What happens on the projective hierarchy and why do we need more to prove the PSP for $\Pi$ classes in comparison to proving it for $\Sigma$ classes? | |
| Oct 23, 2011 at 3:43 | comment | added | Todd Eisworth | Francois, maybe this should be asked as a full-fledged question, but have such "nice" characterizations been obtained further up in the projective hierarachy? My knowledge of descriptive set theory tends to peter out around the $\mathbf{\Sigma}^1_3$ level... | |
| Oct 23, 2011 at 3:21 | history | answered | François G. Dorais | CC BY-SA 3.0 |