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The importance of Π1 0 classes in effective randomness
Journal of Symbolic Logic 75 (1):387-400 (2010)
Abstract
We prove a number of results in effective randomness, using methods in which Π⁰₁ classes play an essential role. The results proved include the fact that every PA Turing degree is the join of two random Turing degrees, and the existence of a minimal pair of LR degrees below the LR degree of the halting problem.Author's Profile
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Citations of this work
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Low upper bounds in the LR degrees.David Diamondstone - 2012 - Annals of Pure and Applied Logic 163 (3):314-320.
Elementary differences between the degrees of unsolvability and degrees of compressibility.George Barmpalias - 2010 - Annals of Pure and Applied Logic 161 (7):923-934.
Algorithmic randomness and measures of complexity.George Barmpalias - 2013 - Bulletin of Symbolic Logic 19 (3):318-350.
References found in this work
Calibrating randomness.Rod Downey, Denis R. Hirschfeldt, André Nies & Sebastiaan A. Terwijn - 2006 - Bulletin of Symbolic Logic 12 (3):411-491.
Almost everywhere domination and superhighness.Stephen G. Simpson - 2007 - Mathematical Logic Quarterly 53 (4):462-482.
Relativizing chaitin's halting probability.Rod Downey, Denis R. Hirschfeldt, Joseph S. Miller & André Nies - 2005 - Journal of Mathematical Logic 5 (02):167-192.
Mass problems and hyperarithmeticity.Joshua A. Cole & Stephen G. Simpson - 2007 - Journal of Mathematical Logic 7 (2):125-143.
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