Degrees with Almost Universal Cupping Property

摘要

The notion of cuppingoncupping has played an essential role in the study of various degree structures in the Ershov hierarchy. As an approach to refute Shoenfield conjecture, Yates (see [2]) proved the existence of a nonzero noncup-pable r.e. degree, a degree cupping no incomplete r.e. degree to 0'. In contrast to this, Arslanov proved in [1] that nonzero noncuppable degrees do not exist in the structure of d.r.e. degrees, which shows that the structures of r.e. degrees and d.r.e. degrees are not elementary equivalent.