The importance of Π1 0 classes in effective randomness

Journal of Symbolic Logic 75 (1):387-400 (2010)
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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.

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Andrew Lewis
Graduate Theological Union

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.
Mass problems and hyperarithmeticity.Joshua A. Cole & Stephen G. Simpson - 2007 - Journal of Mathematical Logic 7 (2):125-143.

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