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A structural dichotomy in the enumeration degrees

Hristo A. Ganchev, Iskander Sh Kalimullin, Joseph S. Miller & Mariya I. Soskova

Journal of Symbolic Logic:1-18 (2020)

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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
Density of the cototal enumeration degrees.Joseph S. Miller & Mariya I. Soskova - 2018 - Annals of Pure and Applied Logic 169 (5):450-462.details Download Export citation Bookmark 4 citations
(2 other versions)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.details Download Export citation Bookmark 43 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
(1 other version)Arithmetical Reducibilities I.Alan L. Selman - 1971 - Mathematical Logic Quarterly 17 (1):335-350.details Download Export citation Bookmark 15 citations
(2 other versions)Reducibility and Completeness for Sets of Integers.Richard M. Friedberg & Hartley Rogers - 1959 - Mathematical Logic Quarterly 5 (7‐13):117-125.details Download Export citation Bookmark 41 citations

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