Timeline for Degrees many-one below $0^\omega$
Current License: CC BY-SA 2.5
7 events
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| Mar 31, 2010 at 9:01 | comment | added | Uri Andrews | Thanks, Joel. I don't really know much about the many-1 degrees within the Turing degree of $0^{\omega}$, which is definitely interesting in it's own right. To be honest, I don't personally know much about the analogous question for any Turing degree above $0$. The intended question was about Turing degrees which contain a set which is many-one reducible to $0^{\omega}$, mostly because I was afraid to broach the issue of the many-one refinement of a single turing degree or to leave the comfort of the Turing degrees entirely. | |
| Mar 31, 2010 at 1:21 | comment | added | Joel David Hamkins | Yes Uri, welcome to MO! I'm not sure what kind of characterization you're looking for, since being many-one reducible to 0^omega seems already like a good characterization, when one is used to thinking about Turing degrees. Do you know already how the m-1 degree of 0^omega interacts with the T-degree of 0^omega? | |
| Mar 30, 2010 at 21:30 | comment | added | François G. Dorais | By the way Uri, welcome to MO and thanks for asking this excellent question! | |
| Mar 30, 2010 at 20:53 | answer | added | Uri Andrews | timeline score: 2 | |
| Mar 30, 2010 at 10:38 | comment | added | Uri Andrews | I mean the Turing degree of the set. This is meant to ask about the interplay between a set being turing above each $0^n$ vs. it being many-one below $0^{\omega}$. The constructions that I've seen of sets turing strictly below $0^{\omega}$ but above each $0^n$ are far from producing many-one reductions from $0^{\omega}$. | |
| Mar 30, 2010 at 10:10 | comment | added | abcdxyz | What do you mean by degrees of set? | |
| Mar 30, 2010 at 10:00 | history | asked | Uri Andrews | CC BY-SA 2.5 |