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The importance of Π1 0 classes in effective randomness

  • George Barmpalias (a1), Andrew E.M. Lewis (a2) and Keng Meng Ng (a3)


We prove a number of results in effective randomness, using methods in which Π1 0 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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