Journal of Symbolic Logic 67 (1):409-437 (2002)

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
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2178/jsl/1190150052
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 53,586
Through your library

References found in this work BETA

Classical Recursion Theory.Peter G. Hinman - 2001 - Bulletin of Symbolic Logic 7 (1):71-73.
Splitting Theorems in Recursion Theory.Rod Downey & Michael Stob - 1993 - Annals of Pure and Applied Logic 65 (1):1-106.

View all 12 references / Add more references

Citations of this work BETA

A Hierarchy of Computably Enumerable Degrees.Rod Downey & Noam Greenberg - 2018 - Bulletin of Symbolic Logic 24 (1):53-89.

Add more citations

Similar books and articles

Bi-Isolation in the D.C.E. Degrees.Guohua Wu - 2004 - Journal of Symbolic Logic 69 (2):409 - 420.
Turing Degrees and Many-One Degrees of Maximal Sets.Manuel Lerman - 1970 - Journal of Symbolic Logic 35 (1):29-40.
1-Reducibility Inside an M-Degree with Maximal Set.E. Herrmann - 1992 - Journal of Symbolic Logic 57 (3):1046-1056.
On the Structures Inside Truth-Table Degrees.Frank Stephan - 2001 - Journal of Symbolic Logic 66 (2):731-770.
Complementation in the Turing Degrees.Theodore A. Slaman & John R. Steel - 1989 - Journal of Symbolic Logic 54 (1):160-176.
Degrees of Unsolvability of Continuous Functions.Joseph S. Miller - 2004 - Journal of Symbolic Logic 69 (2):555 - 584.
Wtt-Degrees and T-Degrees of R.E. Sets.Michael Stob - 1983 - Journal of Symbolic Logic 48 (4):921-930.
The Degrees of Conditional Problems.Su Gao - 1994 - Journal of Symbolic Logic 59 (1):166-181.

Analytics

Added to PP index
2009-01-28

Total views
27 ( #368,900 of 2,348,619 )

Recent downloads (6 months)
1 ( #512,295 of 2,348,619 )

How can I increase my downloads?

Downloads

My notes