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The jump operator on the ω-enumeration degrees

Hristo Ganchev & Ivan N. Soskov

Annals of Pure and Applied Logic 160 (3):289-301 (2009)

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A jump inversion theorem for the enumeration jump.I. N. Soskov - 2000 - Archive for Mathematical Logic 39 (6):417-437.details . We prove a jump inversion theorem for the enumeration jump and a minimal pair type theorem for the enumeration reducibilty. As an application some results of Selman, Case and Ash are obtained. Download Export citation Bookmark 7 citations
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.details Download Export citation Bookmark 21 citations
Jumps of quasi-minimal enumeration degrees.Kevin McEvoy - 1985 - Journal of Symbolic Logic 50 (3):839-848.details Download Export citation Bookmark 18 citations
Then-rea enumeration degrees are dense.Alistair H. Lachlan & Richard A. Shore - 1992 - Archive for Mathematical Logic 31 (4):277-285.details Download Export citation Bookmark 20 citations
Arithmetical Reducibilities I.Alan L. Selman - 1971 - Mathematical Logic Quarterly 17 (1):335-350.details Download Export citation Bookmark 15 citations
Arithmetical Reducibilities I.Alan L. Selman - 1971 - Mathematical Logic Quarterly 17 (1):335-350.details Download Export citation Bookmark 15 citations
How Enumeration Reducibility Yields Extended Harrington Non-Splitting.Mariya I. Soskova & S. Barry Cooper - 2008 - Journal of Symbolic Logic 73 (2):634 - 655.details Download Export citation Bookmark 5 citations
Definability of the jump operator in the enumeration degrees.I. Sh Kalimullin - 2003 - Journal of Mathematical Logic 3 (02):257-267.details 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. Download Export citation Bookmark 16 citations

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