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Journal of Logic and Computation Advance Access originally published online on October 9, 2007
Journal of Logic and Computation 2007 17(6):1235-1255; doi:10.1093/logcom/exm042
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

Genericity and Non-bounding in the Enumeration degrees

Mariya Ivanova Soskova

Department of Pure Mathematics, University of Leeds, Leeds, LS2 9JT, UK E-mail: mariya{at}maths.leeds.ac.uk

Received 18 October 2006.


  Abstract

The structure of the semi lattice of enumeration degrees has been investigated from many aspects. One aspect is the bounding and non-bounding properties of generic degrees. Copestake proved that every 2-generic enumeration degree bounds a minimal pair and conjectured that there exists a 1-generic degree that does not bound a minimal pair. In this paper we verify this longstanding conjecture by constructing such a degree using an infinite injury priority argument.

Keywords: Enumeration reducibility; non-bounding degrees; generic degrees; minimal pairs


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