DEGREE SPECTRA AND CO-SPECTRA OF STRUCTURES

Abstract

Abstract. Given a countable structure A, we dene the degree spectrum DS(A) of A to be the set of all enumeration degrees generated by the pre-sentations 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 de-gree 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. 1.