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Journal of Logic and Computation Advance Access originally published online on August 21, 2007
Journal of Logic and Computation 2007 17(6):1193-1214; doi:10.1093/logcom/exm041
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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

The {omega}-Enumeration Degrees

Ivan N. Soskov

Sofia University, 5 James Bourchier Blvd, 1164 Sofia, Bulgaria.
E-mail: soskov{at}fmi.uni-sofia.bg

Received 19 October 2006.


  Abstract

In the present article we initiate the study of the partial ordering of the {omega}-enumeration degrees. This ordering is a semi-lattice which extends the semi-lattice of the enumeration degrees. The main results include a jump inversion theorem, a density theorem for the {omega}-enumeration degrees below the first jump of the least degree and the lack of minimal {omega}-enumeration degrees.

Keywords: Enumeration reducibility; enumeration jump; jump hierarchies


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