Van Lambalgen's Theorem and High Degrees
Johanna N.Y. Franklin and Frank Stephan
Source: Notre Dame J. Formal Logic Volume 52, Number 2
(2011), 173-185.
Abstract
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.
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Notre Dame Journal of Formal Logic
