Let \(\mathcal A\) be a mathematical structure with an additional relation \(R\). The author is interested in the degree spectrum of \(R\), either among computable copies of \(\mathcal A\) when \((\mathcal A,R)\) is a “natural” structure, or (to make this rigorous) among copies of \((\mathcal A,R)\) computable in a large degree d. He introduces the partial order of degree spectra on a cone and begin the study of these objects. Using a result of Harizanov—that, assuming an effectiveness condition on \(\mathcal A\) and \(R\), if \(R\) is not intrinsically computable, then its degree spectrum contains all c.e. degrees—the author shows that there is a minimal non-trivial degree spectrum on a cone, consisting of the c.e. degrees.