Splitting of 2-computably enumerable degrees with avoiding cones

In this paper we show that for any pair of properly 2-c. e. degrees $\mathbf0<\mathbf d<\mathbf a$ such that there are no c. e. degrees between $\mathbf d$ and $\mathbf a$, the degree $\mathbf a$ is splittable in the class of 2-c. e. degrees avoiding the upper cone of $\mathbf d$. We also study the possibility to characterize such an isolation in terms of splitting.