Notre Dame Journal of Formal Logic 52 (2):173-185 (2011)

We show that van Lambalgen's Theorem fails with respect to recursive randomness and Schnorr randomness for some real in every high degree and provide a full characterization of the Turing degrees for which van Lambalgen's Theorem can fail with respect to Kurtz randomness. However, we also show that there is a recursively random real that is not Martin-Löf random for which van Lambalgen's Theorem holds with respect to recursive randomness
Keywords van Lambalgen's Theorem   Schnorr randomness   recursive randomness   Kurtz randomness
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Reprint years 2011
DOI 10.1215/00294527-1306181
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References found in this work BETA

The Axiomatization of Randomness.Michiel van Lambalgen - 1990 - Journal of Symbolic Logic 55 (3):1143-1167.
Minimal Degrees and the Jump Operator.S. B. Cooper - 1973 - Journal of Symbolic Logic 38 (2):249-271.
Uniform Almost Everywhere Domination.Peter Cholak, Noam Greenberg & Joseph S. Miller - 2006 - Journal of Symbolic Logic 71 (3):1057 - 1072.

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An Application of Recursion Theory to Analysis.Liang Yu - 2020 - Bulletin of Symbolic Logic 26 (1):15-25.

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