On the jump classes of noncuppable enumeration degrees

Abstract

AbstractWe prove that for every Σ20 enumeration degree b there exists a noncuppable Σ20 degree a > 0e such that and . This allows us to deduce, from results on the high/low jump hierarchy in the local Turing degrees and the jump preserving properties of the standard embedding , that there exist Σ20 noncuppable enumeration degrees at every possible—i.e., above low1—level of the high/low jump hierarchy in the context of .