Cupping and noncupping in the enumeration degrees of ∑20 sets Original Research Article

We prove the following three theorems on the enumeration degrees of ∑20 sets. Theorem A: There exists a nonzero noncuppable ∑20enumeration degree. Theorem B: Every nonzeroΔ20enumeration degree is cuppable to0′eby an incomplete total enumeration degree. Theorem C: There exists a nonzero lowΔ20enumeration degree with the anticupping property.