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November 2019 On the Degree Structure of Equivalence Relations Under Computable Reducibility
Keng Meng Ng, Hongyuan Yu
Notre Dame J. Formal Logic 60(4): 733-761 (November 2019). DOI: 10.1215/00294527-2019-0028

Abstract

We study the degree structure of the ω-c.e., n-c.e., and Π10 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 ω-c.e. and n-computably enumerable equivalence relations. We provide computable enumerations of the degrees of ω-c.e., n-c.e., and Π10 equivalence relations. We prove that for all the degree classes considered, upward density holds and downward density fails.

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Keng Meng Ng. Hongyuan Yu. "On the Degree Structure of Equivalence Relations Under Computable Reducibility." Notre Dame J. Formal Logic 60 (4) 733 - 761, November 2019. https://doi.org/10.1215/00294527-2019-0028

Information

Received: 5 November 2017; Accepted: 18 July 2018; Published: November 2019
First available in Project Euclid: 12 September 2019

zbMATH: 07167766
MathSciNet: MR4019870
Digital Object Identifier: 10.1215/00294527-2019-0028

Subjects:
Primary: 03D28
Secondary: 03D45

Rights: Copyright © 2019 University of Notre Dame

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Vol.60 • No. 4 • November 2019
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