Timeline for Sets meeting and avoiding computable sets
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 6, 2023 at 4:35 | vote | accept | Dan Turetsky | ||
| Jan 6, 2023 at 4:35 | comment | added | Dan Turetsky | Ah, of course. Very nice. | |
| Jan 5, 2023 at 19:33 | comment | added | Bjørn Kjos-Hanssen | @JoelDavidHamkins Thanks, Richard Shore told me about that at some point but a reminder was helpful. | |
| Jan 5, 2023 at 19:28 | comment | added | Joel David Hamkins | Fusion is the process when you have a sequence of trees, such that they are refining each other as you go along, but after stage $n$ the first $n$ splitting levels are preserved (so you have to prune quickly enough). In this case, the fusion of the trees is the limit tree. I'm not sure what notion of "uniform" you are using, but there are various notions of spliting requirements etc., and most of the ones I know do implement a version of fusion. Fusion is a substitue for countable closure---the forcing isn't closed, but with fusion, you can nevertheless often get by. | |
| Jan 5, 2023 at 19:23 | comment | added | Bjørn Kjos-Hanssen | @JoelDavidHamkins I think Spector constructed a minimal Turing degree using "uniform" trees and those don't suffice to force bi-immunity. Can you do fusion arguments with those trees? | |
| Jan 5, 2023 at 19:17 | comment | added | Joel David Hamkins | With a Sack real, I would think he did, since that is the main thing to do with Sacks reals and the trees approximating them. | |
| Jan 5, 2023 at 19:15 | comment | added | Bjørn Kjos-Hanssen | @JoelDavidHamkins I don't think he advertised it as such, but maybe. | |
| Jan 5, 2023 at 19:12 | comment | added | Joel David Hamkins | Does he use a fusion argument? | |
| Jan 5, 2023 at 18:46 | history | answered | Bjørn Kjos-Hanssen | CC BY-SA 4.0 |