DEGREE SPECTRA AND CO-SPECTRA OF STRUCTURES

Authors

  • Ivan Soskov

Keywords:

degree spectra, enumeration degrees

Abstract

Given a countable structure A, we define the degree spectrum DS(A) of A to be the set of all enumeration degrees generated by the presentations of A on the natural numbers. The co-spectrum of A is the set of all lower bounds of DS(A). We prove some general properties of the degree spectra, which show that they behave with respect to their co-spectra very much like the cones of enumeration degrees. Among the results are the analogs of Selman's Theorem [14], the Minimal Pair Theorem and the existence of a quasi-minimal enumeration degree.

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Published

2004-12-12

How to Cite

Soskov, I. (2004). DEGREE SPECTRA AND CO-SPECTRA OF STRUCTURES. Ann. Sofia Univ. Fac. Math. And Inf., 96, 45–68. Retrieved from https://annual.uni-sofia.bg/index.php/fmi/article/view/160