(untitled) (Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics, 2004)
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.