Abstract

We investigate the index sets associated with the degree structures of computable sets under the parameterized reducibilities introduced by the authors. We solve a question of Peter Cholakand the first author by proving the fundamental index sets associated with a computable set A, {e : W e ≤ q u A} for q∈ {m, T} are Σ4 0 complete. We also show hat FPT(≤ q n ), that is {e : W e computable and ≡ q n ?}, is Σ4 0 complete. We also look at computable presentability of these classes