Timeline for Double Posner-Robinson Join (or a cupping analog of minimal pair)
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 7, 2023 at 19:34 | vote | accept | Peter Gerdes | ||
| Apr 29, 2023 at 18:23 | comment | added | Joe Miller | Peter: Yes, exactly. The coding is a little trickier because you need all of the sets to simultaneously tell you whether you're forcing truth or falsity. The second and third proofs mentioned in 喻 良's answer use different tricks to ensure that this is possible. | |
| Apr 29, 2023 at 1:18 | answer | added | 喻 良 | timeline score: 5 | |
| Apr 28, 2023 at 19:15 | comment | added | Peter Gerdes | As opposed to the Posner-Robinson approach where we use n plus some fast growing function in C to bound the length of sigma (which won't extend to allowing us to join a hyperimmune free degrees A to arbitrary degree above 0' join A). | |
| Apr 28, 2023 at 19:14 | answer | added | Peter Gerdes | timeline score: 2 | |
| Apr 28, 2023 at 17:27 | comment | added | Peter Gerdes | By Jockusch-Shore style do you mean where we add 0^n^1^\sigma and use membership of n in the set to code whether we force the truth or falsity? | |
| Apr 28, 2023 at 4:29 | comment | added | Joe Miller | I don't know why 喻 良 is being so cheeky. The multiple degree version of Posner–Robinson is Theorem 3 in the Posner–Robinson paper. And he knows of two Jockusch–Shore style proofs (unpublished, as of yet) | |
| Apr 27, 2023 at 11:44 | comment | added | 喻 良 | You may find the answer in the Posner-Robinson's paper. | |
| Apr 27, 2023 at 3:21 | comment | added | Peter Gerdes | I'm guessing that this can be done using the technique of e-splitting extensions in the proof of the complementation theorem to manage to avoid computing $D_1$ but it's complicated enough that I'm not sure. | |
| Apr 27, 2023 at 3:17 | history | asked | Peter Gerdes | CC BY-SA 4.0 |