### Jump operator and Yates degrees

Guohua Wu
Source: J. Symbolic Logic Volume 71, Issue 1 (2006), 252-264.

#### Abstract

In [9], Yates proved the existence of a Turing degree a such that 0, 0’ are the only c.e. degrees comparable with it. By Slaman and Steel [7], every degree below 0’ has a 1-generic complement, and as a consequence, Yates degrees can be 1-generic, and hence can be low. In this paper, we prove that Yates degrees occur in every jump class.

First Page:
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Permanent link to this document: http://projecteuclid.org/euclid.jsl/1140641173
Digital Object Identifier: doi:10.2178/jsl/1140641173
Mathematical Reviews number (MathSciNet): MR2210066
Zentralblatt MATH identifier: 05038898

### References

A. E. M. Lewis, Minimal complements for degrees below 0$'$, Journal of Symbolic Logic, vol. 69 (2002), pp. 937--966.
Mathematical Reviews (MathSciNet): MR2135652
Digital Object Identifier: doi:10.2178/jsl/1102022208
Project Euclid: euclid.jsl/1102022208
Zentralblatt MATH: 1086.03031
P. Odifreddi, Classical recursion theory, Studies in Logic and the Foundations of Mathematics 125, North-Holland, 1989.
Mathematical Reviews (MathSciNet): MR982269
G. E. Sacks, Degrees of unsolvability, Annals of Mathematics Studies, no. 55, Princeton, 1963.
--------, On the degrees less than 0$^(1)$, Annals of Mathematics, vol. 77 (1963), pp. 211--231.
Mathematical Reviews (MathSciNet): MR146078
Digital Object Identifier: doi:10.2307/1970214
D. Seetapun and T. A. Slaman, Minimal complements, manuscript.
J. R. Shoenfield, Mathematical review of paper [yates?].
T. A. Slaman and J. R. Steel, Complementation in the Turing degrees, Journal of Symbolic Logic, vol. 54 (1989), pp. 160--176.
Mathematical Reviews (MathSciNet): MR987329
Digital Object Identifier: doi:10.2307/2275022
Zentralblatt MATH: 0691.03024
R. I. Soare, Recursively enumerable sets and degrees, Springer-Verlag, Berlin, 1987.
Mathematical Reviews (MathSciNet): MR882921
C. E. M. Yates, Recursively enumerable degrees and the degrees less than $0\sp(1)$, Sets, models and recursion theory. Proceedings of the summer school in mathematical logic and tenth logic colloquium, Leicester, 1965, North-Holland, 1967, pp. 264--271.
Mathematical Reviews (MathSciNet): MR219422