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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.
MSC:
03D25 Recursively (computably) enumerable sets and degrees
03D28 Other Turing degree structures
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[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
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