Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 52, Number 2 (2011), 173-185.
Van Lambalgen's Theorem and High Degrees
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.
Notre Dame J. Formal Logic, Volume 52, Number 2 (2011), 173-185.
First available in Project Euclid: 28 April 2011
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03D32: Algorithmic randomness and dimension [See also 68Q30]
Franklin, Johanna N.Y.; Stephan, Frank. Van Lambalgen's Theorem and High Degrees. Notre Dame J. Formal Logic 52 (2011), no. 2, 173--185. doi:10.1215/00294527-1306181. https://projecteuclid.org/euclid.ndjfl/1303995713