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Definability of the jump operator in the enumeration degrees
Journal of Mathematical Logic 3 (02):257-267 (2003)
Abstract
We show that the e-degree 0'e and the map u ↦ u' are definable in the upper semilattice of all e-degrees. The class of total e-degrees ≥0'e is also definable.Author's Profile
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2012-09-02
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2012-09-02
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97 (#537,480)
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32 (#273,677)
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Citations of this work
Density of the cototal enumeration degrees.Joseph S. Miller & Mariya I. Soskova - 2018 - Annals of Pure and Applied Logic 169 (5):450-462.
Turing degrees in Polish spaces and decomposability of Borel functions.Vassilios Gregoriades, Takayuki Kihara & Keng Meng Ng - 2020 - Journal of Mathematical Logic 21 (1):2050021.
Initial segments of the enumeration degrees.Hristo Ganchev & Andrea Sorbi - 2016 - Journal of Symbolic Logic 81 (1):316-325.
The jump operator on the ω-enumeration degrees.Hristo Ganchev & Ivan N. Soskov - 2009 - Annals of Pure and Applied Logic 160 (3):289-301.
A structural dichotomy in the enumeration degrees.Hristo A. Ganchev, Iskander Sh Kalimullin, Joseph S. Miller & Mariya I. Soskova - 2022 - Journal of Symbolic Logic 87 (2):527-544.
References found in this work
Theory of recursive functions and effective computability.Hartley Rogers - 1987 - Cambridge: MIT Press.
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.
Jumps of quasi-minimal enumeration degrees.Kevin McEvoy - 1985 - Journal of Symbolic Logic 50 (3):839-848.
Degrees joining to 0'. [REVIEW]David B. Posner & Robert W. Robinson - 1981 - Journal of Symbolic Logic 46 (4):714 - 722.
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