Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-26T11:12:24.599Z Has data issue: false hasContentIssue false
  • English
  • Français

Jump operator and Yates Degrees

Published online by Cambridge University Press:  12 March 2014

Guohua Wu
Guohua Wu*
Affiliation:
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 639798, Republic of Singapore. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 1 , March 2006 , pp. 252 - 264
Copyright
Copyright © Association for Symbolic Logic 2006

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Lewis, A. E. M., Minimal complements for degrees below 0′, this Journal, vol. 69 (2002), pp. 937–966.Google Scholar
[2]Odifreddi, P., Classical recursion theory, Studies in Logic and the Foundations of Mathematics 125, North-Holland, 1989.Google Scholar
[3]Sacks, G. E., Degrees of unsolvability, Annals of Mathematics Studies, no. 55, Princeton, 1963.Google Scholar
[4]Sacks, G. E., On the degrees less than 0(1), Annals of Mathematics, vol. 77 (1963), pp. 211–231.CrossRefGoogle Scholar
[5]Seetapun, D. and Slaman, T. A., Minimal complements, manuscript.Google Scholar
[6]Shoenfield, J. R., Mathematical review of paper [9].Google Scholar
[7]Slaman, T. A. and Steel, J. R., Complementation in the Turing degrees, this Journal, vol. 54 (1989), pp. 160–176.Google Scholar
[8]Soare, R. I., Recursively enumerable sets and degrees, Springer-Verlag, Berlin, 1987.CrossRefGoogle Scholar
[9]Yates, C. E. M., Recursively enumerable degrees and the degrees less than 0(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.Google Scholar