We examine the relationship between the CEA hierarchy and the Ershov hierarchy within $\Delta_2^0$ Turing degrees. We study the long-standing problem raised in [1] about the existence of a low computably enumerable (c.e.) ...
Abstract: Let $$\simeq$$ be a binary relation between sets of integers, and ≤R be a Post reducibility, i.e. a reflexive and transitive relation between sets of integers such that if A ≤R B then the computational complexity ...
In this work, we review results of the last years related to the development of the structural theory of n-c.e. Turing degrees for n > 1. We also discuss possible approaches to solution of the open problems.