Timeline for Co-cones in the Turing degrees
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Jul 23, 2018 at 18:03 | comment | added | Morteza Azad | (+1) Interesting examples! Thank you, Noah and @Wojowu. | |
| Jul 23, 2018 at 17:51 | comment | added | Noah Schweber | @MortezaAzad Also, determinacy hypotheses can play a role, via Martin's cone theorem. One might be tempted to use Martin's theorem here to give a negative answer on a cone, but it doesn't seem applicable since for the obvious attack we would need to first know that there are only countably many possible isomorphism types of cocones. You can use the cone theorem to show (in ZFC alone, in fact) that the cocones of all sufficiently large ${\bf d}$ are elementarily equivalent, but that's a very weak result. | |
| Jul 22, 2018 at 19:45 | comment | added | Jim Conant | @GerryMyerson: I'd like there to be a dual object to a nant. | |
| Jul 22, 2018 at 16:30 | history | edited | Noah Schweber | CC BY-SA 4.0 |
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| Jul 22, 2018 at 14:03 | comment | added | Noah Schweber | @MortezaAzad See the Slaman-Woodin manuscript linked in my answer; forcing/absoluteness arguments play a crucial role in showing e.g. that the automorphism group of the Turing degrees is at most countable. | |
| Jul 22, 2018 at 8:20 | comment | added | Wojowu | @MortezaAzad One quick example is showing there are incomparable Turing degrees using forcing. | |
| Jul 22, 2018 at 6:34 | comment | added | Morteza Azad | @NoahSchweber Any specific/iconic example of how set theory plays a role in such questions? | |
| Jul 22, 2018 at 5:07 | comment | added | Gerhard Paseman | @Gerry, what makes you so sure that there is no such thing? Gerhard "Doesn't Really Need The Answer" Paseman, 2018.07.21. | |
| Jul 22, 2018 at 4:01 | history | edited | Noah Schweber | CC BY-SA 4.0 |
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| Jul 22, 2018 at 3:59 | comment | added | Gerry Myerson | I'm glad there's no such thing as the dual object to a Jones. | |
| Jul 22, 2018 at 3:30 | comment | added | Noah Schweber | The "set theory" tag is just because of how often set theory manages to sneak into these sorts of questions; it's purely speculative on my part. | |
| Jul 22, 2018 at 3:30 | history | asked | Noah Schweber | CC BY-SA 4.0 |