## Notre Dame Journal of Formal Logic

### $\Pi^0_1$ Classes, Peano Arithmetic, Randomness, and Computable Domination

#### Abstract

We present an overview of the topics in the title and of some of the key results pertaining to them. These have historically been topics of interest in computability theory and continue to be a rich source of problems and ideas. In particular, we draw attention to the links and connections between these topics and explore their significance to modern research in the field.

#### Article information

Source
Notre Dame J. Formal Logic, Volume 51, Number 1 (2010), 127-159.

Dates
First available in Project Euclid: 4 May 2010

https://projecteuclid.org/euclid.ndjfl/1273002114

Digital Object Identifier
doi:10.1215/00294527-2010-009

Mathematical Reviews number (MathSciNet)
MR2666574

Zentralblatt MATH identifier
1197.03045

#### Citation

Diamondstone, David E.; Dzhafarov, Damir D.; Soare, Robert I. $\Pi^0_1$ Classes, Peano Arithmetic, Randomness, and Computable Domination. Notre Dame J. Formal Logic 51 (2010), no. 1, 127--159. doi:10.1215/00294527-2010-009. https://projecteuclid.org/euclid.ndjfl/1273002114

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