Splitting in 2-computably enumerable degrees with avoiding cones

Abstract

In this paper we show that for any pair of properly 2-c. e. degrees 0 < d < a such that there are no c. e. degrees between d and a, the degree a is splittable in the class of 2-c. e. degrees avoiding the upper cone of d. We also study the possibility to characterize such an isolation in terms of splitting.