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Π 1 0 Classes, Peano Arithmetic, Randomness, and Computable Domination
Notre Dame Journal of Formal Logic 51 (1):127-159 (2010)
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 fieldOther Versions
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Citations of this work
Set existence principles and closure conditions: unravelling the standard view of reverse mathematics.Benedict Eastaugh - 2019 - Philosophia Mathematica 27 (2):153-176.
An effectively closed set with no join property.Ahmet Çevik - 2021 - Mathematical Logic Quarterly 67 (3):313-320.
Coarse computability, the density metric, Hausdorff distances between Turing degrees, perfect trees, and reverse mathematics.Denis R. Hirschfeldt, Carl G. Jockusch & Paul E. Schupp - 2023 - Journal of Mathematical Logic 24 (2).
Antibasis theorems for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi^0_1}$$\end{document} classes and the jump hierarchy. [REVIEW]Ahmet Çevik - 2013 - Archive for Mathematical Logic 52 (1-2):137-142.
References found in this work
The Degrees of Hyperimmune Sets.Webb Miller & D. A. Martin - 1968 - Mathematical Logic Quarterly 14 (7-12):159-166.
Members of countable π10 classes.Douglas Cenzer, Peter Clote, Rick L. Smith, Robert I. Soare & Stanley S. Wainer - 1986 - Annals of Pure and Applied Logic 31:145-163.
Ramsey's Theorem and Cone Avoidance.Damir D. Dzhafarov & Carl G. Jockusch - 2009 - Journal of Symbolic Logic 74 (2):557-578.
Lowness for the class of Schnorr random sets.B. Kjös-Hanssen, A. Nies & F. Stephan - 2005 - Notre Dame Journal of Formal Logic 35 (3):647-657.
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