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Journal of Logic and Computation Advance Access originally published online on July 16, 2007
Journal of Logic and Computation 2007 17(6):1215-1233; doi:10.1093/logcom/exm043
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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

Relativized Degree Spectra

Alexandra A. Soskova

Sofia University, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria.

E-mail: asoskova{at}fmi.uni-sofia.bg

Received 19 October 2006.


  Abstract

We present a relativized version of the notion of a degree spectrum of a structure with respect to finitely many abstract structures. We study the connection to the notion of joint spectrum. We prove that some properties of the degree spectrum as a minimal pair theorem and the existence of quasi-minimal degrees are true for the relative spectrum.

Keywords: Enumeration degrees; forcing; degree spectra; recursive {Sigma} +k formulae


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