Journal of Symbolic Logic

Nonexistence of minimal pairs for generic computability

Gregory Igusa

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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 computability, answering a question of Jockusch and Schupp.

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J. Symbolic Logic, Volume 78, Issue 2 (2013), 511-522.

First available in Project Euclid: 15 May 2013

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Igusa, Gregory. Nonexistence of minimal pairs for generic computability. J. Symbolic Logic 78 (2013), no. 2, 511--522. doi:10.2178/jsl.7802090.

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