Degree Spectra of Structures

Alexandra A. Soskova
Sofia University

Abstract

Given a countable  structure A,  the Degree spectrum DS(A) of A  is the set of all
enumeration degrees generated by all presentations of  A on the natural numbers.
The Co-spectrum of A is the set of all lower bounds of
DS(A).
We will present 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 Minimal Pair
Theorem and the existence of a quasi-minimal enumeration degree.
Some  generalized   versions of the notion of  Degree spectrum  with respect to
finitely many abstract structures are presented, possessing  all general and specific
properties of the Degree spectra, inspired by the notion of relatively intrinsic on A
sets.