Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 60, Number 4 (2019), 733-761.
On the Degree Structure of Equivalence Relations Under Computable Reducibility
We study the degree structure of the -c.e., -c.e., and equivalence relations under the computable many-one reducibility. In particular, we investigate for each of these classes of degrees the most basic questions about the structure of the partial order. We prove the existence of the greatest element for the -c.e. and -computably enumerable equivalence relations. We provide computable enumerations of the degrees of -c.e., -c.e., and equivalence relations. We prove that for all the degree classes considered, upward density holds and downward density fails.
Notre Dame J. Formal Logic, Volume 60, Number 4 (2019), 733-761.
Received: 5 November 2017
Accepted: 18 July 2018
First available in Project Euclid: 12 September 2019
Permanent link to this document
Digital Object Identifier
Ng, Keng Meng; Yu, Hongyuan. On the Degree Structure of Equivalence Relations Under Computable Reducibility. Notre Dame J. Formal Logic 60 (2019), no. 4, 733--761. doi:10.1215/00294527-2019-0028. https://projecteuclid.org/euclid.ndjfl/1568253623