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Cupping and noncupping in the enumeration degrees of ∑20 sets
Annals of Pure and Applied Logic 82 (3):317-342 (1996)
Abstract
We prove the following three theorems on the enumeration degrees of ∑20 sets. Theorem A: There exists a nonzero noncuppable ∑20 enumeration degree. Theorem B: Every nonzero Δ20enumeration degree is cuppable to 0′e by an incomplete total enumeration degree. Theorem C: There exists a nonzero low Δ20 enumeration degree with the anticupping propertyOther Versions
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Citations of this work
Initial segments of the enumeration degrees.Hristo Ganchev & Andrea Sorbi - 2016 - Journal of Symbolic Logic 81 (1):316-325.
Cupping and definability in the local structure of the enumeration degrees.Hristo Ganchev & Mariya I. Soskova - 2012 - Journal of Symbolic Logic 77 (1):133-158.
On the jump classes of noncuppable enumeration degrees.Charles M. Harris - 2011 - Journal of Symbolic Logic 76 (1):177 - 197.
The limitations of cupping in the local structure of the enumeration degrees.Mariya I. Soskova - 2010 - Archive for Mathematical Logic 49 (2):169-193.
Structural properties and Σ20 enumeration degrees.André Nies & Andrea Sorbi - 2000 - Journal of Symbolic Logic 65 (1):285-292.
References found in this work
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Reducibility and Completeness for Sets of Integers.Richard M. Friedberg & Hartley Rogers - 1959 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 5 (7-13):117-125.
Reducibility and Completeness for Sets of Integers.Richard M. Friedberg & Hartley Rogers - 1959 - Mathematical Logic Quarterly 5 (7‐13):117-125.
Partial degrees and the density problem. Part 2: The enumeration degrees of the ∑2 sets are dense.S. B. Cooper - 1984 - Journal of Symbolic Logic 49 (2):503 - 513.
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