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Journal of Logic and Computation Advance Access originally published online on September 12, 2008
Journal of Logic and Computation 2009 19(1):199-215; doi:10.1093/logcom/exn024
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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

A Jump Inversion Theorem for the Degree Spectra

Alexandra A. Soskova and Ivan N. Soskov

Faculty of Mathematics and Computer Science, Sofia University, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria.

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

Received 30 September 2007.


  Abstract

In the present article, we continue the study of the properties of the spectra of structures as sets of degrees initiated in [11]. Here, we consider the relationships between the spectra and the jump spectra. Our first result is that every jump spectrum is also a spectrum. The main result sounds like a Jump inversion theorem. Namely, we show that if a spectrum A is contained in the set of the jumps of the degrees in some spectrum B then there exists a spectrum C such that C{subseteq}B and A is equal to the set of the jumps of the degrees in C.

Keywords: Turing degrees; degree spectra; forcing; Marker's extensions; enumerations


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