Cupping and noncupping in the enumeration degrees of ∑ 20 sets

Abstract

We prove the following three theorems on the enumeration degrees of ∑ 2 0 sets. Theorem A: There exists a nonzero noncuppable ∑ 2 0 enumeration degree. Theorem B: Every nonzero Δ 2 0 enumeration degree is cuppable to 0′ e by an incomplete total enumeration degree. Theorem C: There exists a nonzero low Δ 2 0 enumeration degree with the anticupping property.