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Initial segments of the enumeration degrees

Hristo Ganchev & Andrea Sorbi

Journal of Symbolic Logic 81 (1):316-325 (2016)

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Avoiding uniformity in the Δ 2 0 enumeration degrees.Liliana Badillo & Charles M. Harris - 2014 - Annals of Pure and Applied Logic 165 (9):1355-1379.details Defining a class of sets to be uniform Δ02 if it is derived from a binary {0,1}{0,1}-valued function f≤TKf≤TK, we show that, for any C⊆DeC⊆De induced by such a class, there exists a high Δ02 degree c which is incomparable with every degree b ϵ Ce \ {0e, 0'e}. We show how this result can be applied to quite general subclasses of the Ershov Hierarchy and we also prove, as a direct corollary, that every nonzero low degree caps with both (...) Download Export citation Bookmark 2 citations
(1 other version)Cupping and noncupping in the enumeration degrees of ∑20 sets.S. Barry Cooper, Andrea Sorbi & Xiaoding Yi - 1996 - Annals of Pure and Applied Logic 82 (3):317-342.details 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 property. Download Export citation Bookmark 13 citations
A non-splitting theorem in the enumeration degrees.Mariya Ivanova Soskova - 2009 - Annals of Pure and Applied Logic 160 (3):400-418.details We complete a study of the splitting/non-splitting properties of the enumeration degrees below by proving an analog of Harrington’s non-splitting theorem for the enumeration degrees. We show how non-splitting techniques known from the study of the c.e. Turing degrees can be adapted to the enumeration degrees. Download Export citation Bookmark 3 citations
On extensions of embeddings into the enumeration degrees of the -sets.Steffen Lempp, Theodore A. Slaman & Andrea Sorbi - 2005 - Journal of Mathematical Logic 5 (02):247-298.details We give an algorithm for deciding whether an embedding of a finite partial order [Formula: see text] into the enumeration degrees of the [Formula: see text]-sets can always be extended to an embedding of a finite partial order [Formula: see text]. Download Export citation Bookmark 5 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)S. Barry Cooper, Computability Theory: Chapman & Hall/crc, 2003, US$ 76.95, 424 pp., ISBN-10: 1584882379, ISBN-13: 978-1584882374, hardcover. Dimensions (in inches): 9.7 × 6.2 × 1.1. [REVIEW]Lars Kristiansen - 2007 - Studia Logica 86 (1):145-146.details Download Export citation Bookmark 12 citations

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