Computational randomness and lowness

Journal of Symbolic Logic 66 (3):1199-1205 (2001)
We prove that there are uncountably many sets that are low for the class of Schnorr random reals. We give a purely recursion theoretic characterization of these sets and show that they all have Turing degree incomparable to 0'. This contrasts with a result of Kučera and Terwijn [5] on sets that are low for the class of Martin-Löf random reals
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DOI 10.2307/2695101
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Keng Meng Ng (2008). On Strongly Jump Traceable Reals. Annals of Pure and Applied Logic 154 (1):51-69.
Rutger Kuyper (2013). Natural Factors of the Muchnik Lattice Capturing IPC. Annals of Pure and Applied Logic 164 (10):1025-1036.

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