The Journal of Symbolic Logic

Research Article

Jump operator and Yates Degrees

Guohua Wu *

Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 639798, Republic of Singapore. E-mail: guohua@ntu.edu.sg

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.

(Received June 07 2005)

(Accepted October 29 2005)

Footnotes

*   The author is partially supported by a start-up grant No. M48110008 from NTU and the International Joint Project No. 60310213 of NSF Cof China. The author wants to thank the anonymous referee for several significant suggestions.