Comparing the degrees of enumerability and the closed Medvedev degrees

Abstract

We compare the degrees of enumerability and the closed Medvedev degrees and find that many situations occur. There are nonzero closed degrees that do not bound nonzero degrees of enumerability, there are nonzero degrees of enumerability that do not bound nonzero closed degrees, and there are degrees that are nontrivially both degrees of enumerability and closed degrees. We also show that the compact degrees of enumerability exactly correspond to the cototal enumeration degrees.

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Item Type:	Article
Authors/Creators:	Shafer, P https://orcid.org/0000-0001-5386-9218 Sorbi, A
Copyright, Publisher and Additional Information:	© The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Keywords:	Medvedev degrees; Enumeration degrees
Dates:	Accepted: 15 September 2018 Published (online): 28 September 2018 Published: August 2019
Institution:	The University of Leeds
Academic Units:	The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds)
Depositing User:	Symplectic Publications
Date Deposited:	07 Nov 2018 14:02
Last Modified:	12 Jul 2019 09:02
Status:	Published
Publisher:	Springer
Identification Number:	10.1007/s00153-018-0648-x
Open Archives Initiative ID (OAI ID):	oai:eprints.whiterose.ac.uk:138229

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Comparing the degrees of enumerability and the closed Medvedev degrees

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