Splitting and nonsplitting in the [formula omitted] enumeration degrees

Abstract

This paper continues the project, initiated in (Arslanov, Cooper and Kalimullin 2003) [3], of describing general conditions under which relative splittings are derivable in the local structure of the enumeration degrees, for which the Ershov hierarchy provides an informative setting. The main results below include a proof that any high total e -degree below 0 e ′ is splittable over any low e -degree below it, a non-cupping result in the high enumeration degrees which occurs at a low level of the Ershov hierarchy, and a 0̸ ‴ -priority construction of a Π 1 0 e -degree unsplittable over a 3-c.e. e -degree below it.