Open Access
2011 Van Lambalgen's Theorem and High Degrees
Johanna N.Y. Franklin, Frank Stephan
Notre Dame J. Formal Logic 52(2): 173-185 (2011). DOI: 10.1215/00294527-1306181


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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Johanna N.Y. Franklin. Frank Stephan. "Van Lambalgen's Theorem and High Degrees." Notre Dame J. Formal Logic 52 (2) 173 - 185, 2011.


Published: 2011
First available in Project Euclid: 28 April 2011

zbMATH: 1223.03024
MathSciNet: MR2794650
Digital Object Identifier: 10.1215/00294527-1306181

Primary: 03D32

Keywords: Kurtz randomness , recursive randomness , Schnorr randomness , van Lambalgen's Theorem

Rights: Copyright © 2011 University of Notre Dame

Vol.52 • No. 2 • 2011
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