The degrees of bi-hyperhyperimmune sets

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Annals of Pure and Applied Logic 165 (3):803-811 (2014)
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Abstract

We study the degrees of bi-hyperhyperimmune sets. Our main result characterizes these degrees as those that compute a function that is not dominated by any ∆02 function, and equivalently, those that compute a weak 2-generic. These characterizations imply that the collection of bi-hhi Turing degrees is closed upwards

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10.1016/j.apal.2013.10.004

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References found in this work

The Degrees of Hyperimmune Sets.Webb Miller & D. A. Martin - 1968 - Mathematical Logic Quarterly 14 (7-12):159-166.
The degrees of bi‐immune sets.Carl G. Jockusch - 1969 - Mathematical Logic Quarterly 15 (7‐12):135-140.
Notions of weak genericity.Stuart A. Kurtz - 1983 - Journal of Symbolic Logic 48 (3):764-770.
The degrees of bi-immune sets.Carl G. Jockusch - 1969 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 15 (7-12):135-140.

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