Journal of Symbolic Logic

Bounding and nonbounding minimal pairs in the enumeration degrees

S. Barry Cooper, Angsheng Li, Andrea Sorbi, and Yue Yang

Full-text: Access denied (no subscription detected)

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

Abstract

We show that every nonzero Δ⁰₂ e-degree bounds a minimal pair. On the other hand, there exist Σ⁰₂ e-degrees which bound no minimal pair.

Article information

Source
J. Symbolic Logic, Volume 70, Issue 3 (2005), 741-766.

Dates
First available in Project Euclid: 22 July 2005

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1122038912

Digital Object Identifier
doi:10.2178/jsl/1122038912

Mathematical Reviews number (MathSciNet)
MR2155264

Zentralblatt MATH identifier
1093.03029

Subjects
Primary: 03D30: Other degrees and reducibilities

Citation

Cooper, S. Barry; Li, Angsheng; Sorbi, Andrea; Yang, Yue. Bounding and nonbounding minimal pairs in the enumeration degrees. J. Symbolic Logic 70 (2005), no. 3, 741--766. doi:10.2178/jsl/1122038912. https://projecteuclid.org/euclid.jsl/1122038912


Export citation

References

  • M. Arslanov, S. Barry Cooper, and I. S. Kalimullin Splitting properties of total e-degrees, Algebra and Logic, vol. 42 (2003), pp. 1--13.
  • S. B. Cooper Partial degrees and the density problem, Journal of Symbolic Logic, vol. 47 (1982), pp. 854--859.
  • K. Copestake $1$-genericity in the enumeration degrees, Journal of Symbolic Logic,(1988), no. 53, pp. 878--887.
  • R. M. Friedberg and H. Rogers, Jr Reducibility and completeness for sets of integers, Zeitschrift für Mathenatische Logik und Grundlagen der Mathematik, vol. 5 (1959), pp. 117--125.
  • L. Gutteridge Some results on enumeration reducibility, Ph.D. thesis, Simon Fraser University,1971.
  • A. Lachlan Bounding minimal pairs, Journal of Symbolic Logic, vol. 44 (1979), pp. 626--642.
  • K. McEvoy and S. B. Cooper On minimal pairs of enumeration degrees, Journal of Symbolic Logic, vol. 50 (1985), pp. 983--1001.
  • R. Shore and A. Sorbi Jumps of $\Sigma^0_2$ high e-degrees and properly $\Sigma^0_2$ e-degrees, Recursion Theory and Complexity (M. Arslanov and S. Lempp, editors), de Gruyter Series in Logic and its Applications, W. de Gruyter, Berlin, New York,1999, pp. 157--172.
  • R. I. Soare Recursively Enumerable Sets and Degrees, Perspectives in Mathematical Logic, Omega Series, Springer-Verlag, Heidelberg,1987.