Timeline for "Effective gaps" in the c.e. degrees

5 events

when toggle format	what		by	license	comment
Apr 28 at 19:49	history	edited	Noah Schweber	CC BY-SA 4.0	added 485 characters in body
Apr 27 at 20:10	comment	added	Noah Schweber		@StevenStadnicki Certainly it's easy to embed $\omega+\omega^$ in any interval, just using Sacks density. The issue is the second bulletpoint, the "unfillability" - put another way, I see no easy way to prevent an embedding $f:\omega+\omega^\rightarrow\mathcal{R}$ from extending to an embedding $g: \omega+1+\omega^*\rightarrow\mathcal{R}$. (Here $\mathcal{R}$ is the set of c.e. Turing degrees.)
Apr 27 at 20:05	comment	added	Steven Stadnicki		I suspect you might be able to modify the proof of the special case (of the theorem that all countable linear orders are embeddable in the c.e. degrees) that $\omega+\omega^*$ is embeddable to at least show that effective gaps exist.
Apr 27 at 19:11	history	edited	Noah Schweber	CC BY-SA 4.0	added 60 characters in body
Apr 27 at 18:57	history	asked	Noah Schweber	CC BY-SA 4.0