Degree spectra of relations on structures of finite computable dimension Original Research Article

We show that for every computably enumerable (c.e.) degree View the MathML source there is an intrinsically c.e. relation on the domain of a computable structure of computable dimension 2 whose degree spectrum is View the MathML source, thus answering a question of Goncharov and Khoussainov (Dokl. Math. 55 (1997) 55–57). We also show that this theorem remains true with α-c.e. in place of c.e. for any α∈ω∪{ω}. A modification of the proof of this result similar to what was done in Hirschfeldt (J. Symbolic Logic, to appear) shows that for any α∈ω∪{ω} and any α-c.e. degrees View the MathML source there is an intrinsically α-c.e. relation on the domain of a computable structure of computable dimension n+1 whose degree spectrum is View the MathML source. These results also hold for m-degree spectra of relations.