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"... We prove the following three theorems on the enumeration degrees of # 0 2 sets. Theorem A: There exists a nonzero noncuppable # 0 2 enumeration degree. Theorem B: Every nonzero # 0 2 enumeration degree is cuppable to 0 # e by an incomplete total enumeration degree. Theorem C: There exists a nonzero ..."

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