A structural dichotomy in the enumeration degrees

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Journal of Symbolic Logic:1-18 (2020)
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Abstract

We give several new characterizations of the continuous enumeration degrees. The main one proves that an enumeration degree is continuous if and only if it is not half a nontrivial relativized K-pair. This leads to a structural dichotomy in the enumeration degrees.

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10.1017/jsl.2019.72

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reprint Ganchev, Hristo A.; Kalimullin, Iskander Sh; Miller, Joseph S.; Soskova, Mariya I. (2022) "A structural dichotomy in the enumeration degrees". Journal of Symbolic Logic 87(2):527-544

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References found in this work

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.
Definability of the jump operator in the enumeration degrees.I. Sh Kalimullin - 2003 - Journal of Mathematical Logic 3 (02):257-267.
Arithmetical Reducibilities I.Alan L. Selman - 1971 - Mathematical Logic Quarterly 17 (1):335-350.
Density of the cototal enumeration degrees.Joseph S. Miller & Mariya I. Soskova - 2018 - Annals of Pure and Applied Logic 169 (5):450-462.

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