Journal of Symbolic Logic

Maximal contiguous degrees

Peter Cholak, Rod Downey, and Stephen Walk

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

A computably enumerable (c.e.) degree is a maximal contiguous degree if it is contiguous and no c.e. degree strictly above it is contiguous. We show that there are infinitely many maximal contiguous degrees. Since the contiguous degrees are definable, the class of maximal contiguous degrees provides the first example of a definable infinite anti-chain in the c.e. degrees. In addition, we show that the class of maximal contiguous degrees forms an automorphism base for the c.e. degrees and therefore for the Turing degrees in general. Finally we note that the construction of a maximal contiguous degree can be modified to answer a question of Walk about the array computable degrees and a question of Li about isolated formulas

Article information

Source
J. Symbolic Logic Volume 67, Issue 1 (2002), 409-437.

Dates
First available in Project Euclid: 18 September 2007

Permanent link to this document
http://projecteuclid.org/euclid.jsl/1190150052

Mathematical Reviews number (MathSciNet)
MR1889559

Digital Object Identifier
doi:10.2178/jsl/1190150052

Zentralblatt MATH identifier
1007.03041

Subjects
Primary: 03D25: Recursively (computably) enumerable sets and degrees

Citation

Cholak, Peter; Downey, Rod; Walk, Stephen. Maximal contiguous degrees. Journal of Symbolic Logic 67 (2002), no. 1, 409--437. doi:10.2178/jsl/1190150052. http://projecteuclid.org/euclid.jsl/1190150052.


Export citation