Please use this identifier to cite or link to this item: https://doi.org/10.1215/00294527-1306181
Title: Van Lambalgen's theorem and high degrees
Authors: Franklin, J.N.Y.
Stephan, F. 
Keywords: Kurtz randomness
Recursive randomness
Schnorr randomness
Van Lambalgen's Theorem
Issue Date: 2011
Citation: Franklin, J.N.Y., Stephan, F. (2011). Van Lambalgen's theorem and high degrees. Notre Dame Journal of Formal Logic 52 (2) : 173-185. ScholarBank@NUS Repository. https://doi.org/10.1215/00294527-1306181
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. © 2011 by University of Notre Dame.
Source Title: Notre Dame Journal of Formal Logic
URI: http://scholarbank.nus.edu.sg/handle/10635/104446
ISSN: 00294527
DOI: 10.1215/00294527-1306181
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