Badillo, L, Harris, CM and Soskova, MI (2018) Enumeration 1-Genericity in the Local Enumeration Degrees. Notre Dame Journal of Formal Logic, 59 (4). pp. 461-489. ISSN 0029-4527
Abstract
We discuss a notion of forcing that characterizes enumeration 1-genericity, and we investigate the immunity, lowness, and quasiminimality properties of enumeration 1-generic sets and their degrees. We construct an enumeration operator Δ such that, for any A, the set ΔA is enumeration 1-generic and has the same jump complexity as A. We deduce from this and other recent results from the literature that not only does every degree a bound an enumeration 1-generic degree b such that a'=b', but also that, if a is nonzero, then we can find such b satisfying 0e<b<a. We conclude by proving the existence of both a nonzero low and a properly Σ02 nonsplittable enumeration 1-generic degree, hence proving that the class of 1-generic degrees is properly subsumed by the class of enumeration 1-generic degrees.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 by University of Notre Dame. This is an author produced version of a paper accepted for publication in Notre Dame Journal of Formal Logic. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | enumeration; reducibility; degrees; genericity |
Dates: |
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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: | 09 Aug 2016 13:18 |
Last Modified: | 12 Dec 2018 15:22 |
Status: | Published |
Publisher: | Duke University Press |
Identification Number: | 10.1215/00294527-2018-0008 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:103520 |