Degree spectra of intrinsically c.e. relations

Abstract

AbstractWe show that for every c.e. degreea>0there exists an intrinsically c.e. relation on the domain of a computable structure whose degree spectrum is {0, a}. This result can be extended in two directions. First we show that for every uniformly c.e. collection of setsSthere exists an intrinsically c.e. relation on the domain of a computable structure whose degree spectrum is the set of degrees of elements ofS. Then we show that ifα∈ω∪ {ω} then for anyα-c.e. degreea>0there exists an intrinsicallyα-c.e. relation on the domain of a computable structure whose degree spectrum {0, a}. All of these results also hold for m-degree spectra of relations.