Abstract: Downey, Khoussainov, Miller, and Yu examined degree spectra of unary relations on the structure (ω,<). We extend their results in several directions. First, we show that the degree spectrum of any unary relation on (ω,<) contains only the computable degree or consists of exactly the Δ2 degrees. We then show, using results from combinatorics, that the degree spectrum of an n-ary relation on (ω,<) either contains only the computable degree or contains all c.e. degrees. Finally, we examine unary relations on general computable ordinals and show that the degree spectrum always contains a maximum degree and that degree is always a (possibly infinite) iterate of the jump.