About Segment Complexity of Turing Reductions
Valeriy K. Bulitko · Mathematical logic quarterly · 1999
Abstract We apply complexity concepts to define a new sort of sub‐Turing reducibilities ≤ 𝔷 make the degree hierarchy thinner and to obtain some new specifications of the well known jump inversion theorem of Friedberg. We show that this theorem doesn't hold when ≤ T is replaced with ≤ 𝔷, where 𝔷 is any countable subset of the class 𝔷 of all total increasing functions f : ℕ → ℕ.