Journal of Symbolic Logic

On the jump classes of noncuppable enumeration degrees

Charles M. Harris

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We prove that for every Σ02 enumeration degree b there exists a noncuppable Σ02 degree a > 0e such that b'c a' and a''c b''. 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 ι : 𝒟T → 𝒟e, that there exist Σ02 noncuppable enumeration degrees at every possible—i.e., above low1—level of the high/low jump hierarchy in the context of 𝒟e.

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J. Symbolic Logic, Volume 76, Issue 1 (2011), 177-197.

First available in Project Euclid: 4 January 2011

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Harris, Charles M. On the jump classes of noncuppable enumeration degrees. J. Symbolic Logic 76 (2011), no. 1, 177--197. doi:10.2178/jsl/1294170994.

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