Decomposability of Low 2-Computably Enumerable Degrees and Turing Jumps in the Ershov Hierarchy

摘要

In this paper we prove the following theorem: For every notation of a constructive ordinal there exists a low 2-computably enumerable degree that is not splittable into two lower 2-computably enumerable degrees whose jumps belong to the corresponding Δ-level of the Ershov hierarchy.