Degrees of relations on ordinals

Matthew Wright
2018 Computability - The Journal of the Assosiation  
showed that the degree spectrum of any computable unary relation on (ω, <) either contains only the computable degree, or contains ∅ ′ -that is, if the relation is not intrinsically computable, then it contains ∅ ′ . However, their proof does not extend to n-ary relations, nor does it extend to relations on structures other than ω. We will show that their results can be extended in both of these directions, first by showing that the same result holds for n-ary relations on ω, and then showing
more » ... and then showing that a more general version holds of unary relations on arbitrary computable ordinals. The first extension of the original result is as follows:
doi:10.3233/com-180086 fatcat:enddljyruzhqlbslvqovka2mjy