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Journal of Logic and Computation Advance Access originally published online on October 1, 2008
Journal of Logic and Computation 2009 19(1):151-158; doi:10.1093/logcom/exn032
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© The Author, 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

This article appears in the following Journal of Logic and Computation issue: Special Issue: Logic and Computation in the Real World: CiE 2007 [View the issue table of contents]

Original Articles

Enumeration Degrees and Enumerability of Familes

Iskander Kalimullin *

Kazan State University, Kazan, 420008, Kremlevskaya str. 18, Russia.
E-mail: Iskander.Kalimullin{at}ksu.ru

Received 9 January 2008.


  Abstract

We study the enumerability of families relative to the enumeration degrees. It is shown that if a family of finite sets is e-reducible to every non-zero e-degree, then the family is computably enumerable (c.e). On the another hand, we will find a non-c.e. family which is e-reducible to all non-zero e-degree. This allows to construct a model, whose (extended) degree spectrum coincides with the non-zero e-degrees.

Keywords: c.e. Families; turing degrees; e-degrees (enumeration degrees); degree spectra of models

*Supported by RFBR grant 05-01-00605 and President RF grant MK-4314.2008.1


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