“…It was shown in [14] that if the language is finite, then that degree must be 0. On the other hand, Knight [19] proved that for an automorphically nontrivial structure A, we have that DgSp(A) is closed upwards, that is, if b ∈ DgSp(A) and d > b, then d ∈ DgSp(A). Hirschfeldt, Khoussainov, Shore, and Slinko established in [15] that for every automorphically nontrivial structure A, there is a symmetric irreflexive graph, a partial order, a lattice, a ring, an integral domain of arbitrary characteristic, a commutative semigroup, or a 2-step nilpotent group whose degree spectrum coincides with DgSp(A).…”