Journal of Symbolic Logic

On a problem of Cooper and Epstein

Shamil Ishmukhametov

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


In “Bounding minimal degrees by computably enumerable degrees” by A. Li and D. Yang, (this Journal, \cite{LY}), the authors prove that there exist non-computable computably enumerable degrees c > a > z such that any minimal degree m being below c is also below a. We analyze the proof of their result and show that the proof contains a mistake. Instead we give a proof for the opposite result.

Article information

J. Symbolic Logic, Volume 68, Issue 1 (2003), 52-64.

First available in Project Euclid: 21 February 2003

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Ishmukhametov, Shamil. On a problem of Cooper and Epstein. J. Symbolic Logic 68 (2003), no. 1, 52--64. doi:10.2178/jsl/1045861506.

Export citation


  • S. B. Cooper The strong anticupping property for recursively enumerable degrees, Journal of Symbolic Logic, vol. 54 (1989), pp. 527--539.
  • S. B. Cooper and R. Epstein Complementing below recursively enumerable degrees, Annals of Pure and Applied Logic, vol. 34 (1987), pp. 15--32.
  • R. Downey and M. Stob Minimal pairs in initial segments of the recursively enumerable degrees, Israel Journal of Mathematics, vol. 100 (1997), pp. 7--27.
  • R.L. Epstein Minimal degrees of unsolvability and the full approximation construction, Memoirs of the American Mathematical Society, no. 162,1975.
  • A. Li and D. Yang Bounding minimal degrees by computably enumerable degrees, Journal of Symbolic Logic, vol. 63 (1998), pp. 1319--1347.
  • D. Seetapun and T. Slaman Minimal complements, unpublished manuscript,1992.
  • T. Slaman and J.R. Steel Complementation in the Turing degrees, Journal of Symbolic Logic, vol. 54 (1989), pp. 160--176.
  • R.I. Soare Recursively enumerable sets and degrees, Springer-Verlag, Berlin,1987.
  • C. Spector On degrees of recursive unsolvability, Annals of Mathematics. Second Series, vol. 64 (1956), pp. 581--592.
  • C. E. M. Yates Initial segments of the degrees of unsolvability. part II. Minimal degrees, Journal of Symbolic Logic, vol. 35 (1970), pp. 243--266.