## Journal of Symbolic Logic

### Nonexistence of minimal pairs for generic computability

Gregory Igusa

#### 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

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