Journal of Symbolic Logic

Nonexistence of minimal pairs for generic computability

Gregory Igusa

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 15 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1368627062

Digital Object Identifier
doi:10.2178/jsl.7802090

Mathematical Reviews number (MathSciNet)
MR3145193

Zentralblatt MATH identifier
1302.03048

Citation

Igusa, Gregory. Nonexistence of minimal pairs for generic computability. J. Symbolic Logic 78 (2013), no. 2, 511--522. doi:10.2178/jsl.7802090. https://projecteuclid.org/euclid.jsl/1368627062


Export citation