Notre Dame Journal of Formal Logic

Π 1 0 Classes, Peano Arithmetic, Randomness, and Computable Domination

David E. Diamondstone, Damir D. Dzhafarov, and Robert I. Soare

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

Permanent link to this document
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

Subjects
Primary: 03D30: Other degrees and reducibilities
Secondary: 03C62: Models of arithmetic and set theory [See also 03Hxx] 03D25: Recursively (computably) enumerable sets and degrees 03D32: Algorithmic randomness and dimension [See also 68Q30]

Keywords
Pi01 classes basis theorems Peano arithmetic randomness computable domination hyperimmunity

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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