Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-16T15:25:38.213Z Has data issue: false hasContentIssue false
  • English
  • Français

Wtt-degrees and T-degrees of r.e. sets

Published online by Cambridge University Press:  12 March 2014

Michael Stob
Michael Stob*
Affiliation:
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
*
Calvin College, Grand Rapids, Michigan 49506
Get access Rights & Permissions [Opens in a new window]

Abstract

We use some simple facts about the wtt-degrees of r.e. sets together with a construction to answer some questions concerning the join and meet operators in the r.e. degrees. The construction is that of an r.e. Turing degree a with just one wtt-degree in a such that a is the join of a minimal pair of r.e. degrees. We hope to illustrate the usefulness of studying the stronger reducibility orderings of r.e. sets for providing information about Turing reducibility.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 48 , Issue 4 , December 1983 , pp. 921 - 930
Copyright
Copyright © Association for Symbolic Logic 1983

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

Cohen, P.F. [1975], Weak truth table reducibility and the S point wise ordering of 1–1 recursive functions, Doctoral Dissertation, University of Illinois, Champaign-Urbana, Illinois.Google Scholar
Harrington, L. and Shelah, S. [1982], The undecidability of the recursively enumerable degrees, Bulletin (New Series) of the American Mathematical Society, vol. 6, pp. 79–80.CrossRefGoogle Scholar
Jockusch, C.G. Jr. [1972], Degrees in which the recursive sets are uniformly recursive, Canadian Journal of Mathematics, vol. 24, pp. 1092–1099.CrossRefGoogle Scholar
Kallibekov, S. [1971], Index sets and degrees of unsolvability, Algebra i Logika, vol. 10, pp. 316–326. (Russian)Google Scholar
Lachlan, A.H. [1966], Lower bounds for pairs of recursively enumerable degrees, Proceedings of the London Mathematical Society, ser. 3, vol. 16, pp. 537–569.CrossRefGoogle Scholar
Lachlan, A.H. [1972], Embedding nondistributive lattices in the recursively enumerable degrees, Conference in Mathematical Logic—London '70, Lecture Notes in Mathematics, vol. 255, Springer-Verlag, Berlin, pp. 149–177.CrossRefGoogle Scholar
Lachlan, A.H. [1975], A recursively enumerable degree which will not split over all lesser ones, Annals of Mathematical Logic, vol. 9, pp. 307–365.CrossRefGoogle Scholar
Ladner, R.E. and Sasso, L.P. [1975], The weak truth table degrees of recursively enumerable sets, Annals of Mathematical Logic, vol. 8, pp. 429–448.CrossRefGoogle Scholar
Rogers, H. Jr. [1967], Theory of recursive functions and effective computability, McGraw-Hill, New York.Google Scholar
Yates, C.E.M. [1966], A minimal pair of recursively enumerable degrees, this Journal, vol. 31, pp. 159–168.Google Scholar