Sub-Turing reducibilities of restricted complexity (Q1311145)

The author uses enumerable classes of nondecreasing total functions for defining sub-Turing reducibilities on sets of natural numbers. Some results on such reducibilities are proved. For example, the set of these reducibilities is partially ordered, and it is proved that any partial order is isomorphic to some fragment of the set. Some criteria of \(T\)- and \(wT\)-completeness are formulated.