zbMATH — the first resource for mathematics

Jump operator and Yates degrees. (English) Zbl 1140.03019
C. E. M. Yates [in: J. N. Crossley (ed.), Sets, Models, Recursion Theory, Proc. Summer School Math. Logic, Xth Logic Colloquium Leicester 1965, 264–271 (1967; Zbl 0204.01501)] proved that there is an incomplete degree a such that 0 and \({\mathbf 0}'\) are the only c.e. degrees comparable with a. We call such a degree a Yates degree. In this paper it is proved that Yates degrees occur in all jump classes.
03D25 Recursively (computably) enumerable sets and degrees
03D28 Other Turing degree structures
Full Text: DOI
[1] Sets, models and recursion theory. Proceedings of the summer school in mathematical logic and tenth logic colloquium, Leicester, 1965 pp 264– (1967)
[2] Recursively enumerable sets and degrees (1987)
[3] Complementation in the Turing degrees 54 pp 160– (1989)
[4] Minimal complements for degrees below 0’ 69 pp 937– (2002)
[5] Degrees of unsolvability (1963) · Zbl 0143.25302
[6] Classical recursion theory (1989)
[7] DOI: 10.2307/1970214 · Zbl 0118.25104
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.