Degrees of categoricity of computable structures

Abstract

Defining the degree of categoricity of a computable structure M to be the least degree d for which M is d-computably categorical, we investigate which Turing degrees can be realized as degrees of categoricity. We show that for all n, degrees d. c. e. in and above 0(n) can be so realized, as can the degree 0(ω). © 2009 Springer-Verlag.