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The Journal of Symbolic Logic, 2011
We prove that for every Σ2 0 enumeration degree b there exists a noncuppable Σ2 0 degree a > 0... more We prove that for every Σ2 0 enumeration degree b there exists a noncuppable Σ2 0 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 Σ2 0 noncuppable enumeration degrees at every possible—i.e., above low1—level of the high/low jump hierarchy in the context of .
The Journal of Symbolic Logic, 2011
We prove that for every Σ2 0 enumeration degree b there exists a noncuppable Σ2 0 degree a > 0... more We prove that for every Σ2 0 enumeration degree b there exists a noncuppable Σ2 0 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 Σ2 0 noncuppable enumeration degrees at every possible—i.e., above low1—level of the high/low jump hierarchy in the context of .