Joining to High Degrees
Cholak, Groszek and Slaman proved in  that there is a nonzero computably enumerable (c.e.) degree cupping every low c.e. degree to a low c.e. degree. In the same paper, they pointed out that every nonzero c.e. degree can cup a low2 c.e. degree to a nonlow2 degree. In , Jockusch, Li and Yang improved the latter result by showing that every nonzero c.e. degree c is cuppable to a high c.e. degree by a low2 c.e. degree b. It is natural to ask in which subclass of low2 c.e. degrees b in  can be located. Wu proved  that b can be cappable. We prove in this paper that b in Jockusch, Li and Yang’s result can be noncuppable, improving both Jockusch, Li and Yang, and Wu’s results.
Unable to display preview. Download preview PDF.
- 3.Liu, J., Wu, G.: Joining to high degrees via noncuppables (in preparation)Google Scholar
- 4.Miller, D.: High recursively enumerable degrees and the anti-cupping property. In: Lerman, Schmerl, Soare (eds.) Logic Year 1979-80: University of Connecticut. Lecture Notes in Mathematics, vol. 859, pp. 230–245 (1981)Google Scholar
- 5.Soare, R.I.: Recursively enumerable sets and degrees. Springer, Heidelberg (1987)Google Scholar