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  1. Nonexistence of Minimal Pairs for Generic Computability.Gregory Igusa - 2013 - Journal of Symbolic Logic 78 (2):511-522.
    A generic computation of a subset $A$ of $\mathbb{N}$ consists of a computation that correctly computes most of the bits of $A$, and never incorrectly computes any bits of $A$, but which does not necessarily give an answer for every input. The motivation for this concept comes from group theory and complexity theory, but the purely recursion theoretic analysis proves to be interesting, and often counterintuitive. The primary result of this paper is that there are no minimal pairs for generic (...)
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  • The Degrees of Bi-Hyperhyperimmune Sets.Uri Andrews, Peter Gerdes & Joseph S. Miller - 2014 - Annals of Pure and Applied Logic 165 (3):803-811.
    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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  • Asymptotic Density and the Ershov Hierarchy.Rod Downey, Carl Jockusch, Timothy H. McNicholl & Paul Schupp - 2015 - Mathematical Logic Quarterly 61 (3):189-195.
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  • The Computational Content of Intrinsic Density.Eric P. Astor - 2018 - Journal of Symbolic Logic 83 (2):817-828.
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  • Coarse Reducibility and Algorithmic Randomness.Denis R. Hirschfeldt, Carl G. Jockusch, Rutger Kuyper & Paul E. Schupp - 2016 - Journal of Symbolic Logic 81 (3):1028-1046.
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