A structural dichotomy in the enumeration degrees

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Journal of Symbolic Logic 87 (2):527-544 (2022)
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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 of a nontrivial relativized $\mathcal {K}$ -pair. This leads to a structural dichotomy in the enumeration degrees.

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10.1017/jsl.2019.72

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References found in this work

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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.

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