Notre Dame Journal of Formal Logic

Van Lambalgen's Theorem and High Degrees

Johanna N.Y. Franklin and Frank Stephan

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

Source
Notre Dame J. Formal Logic Volume 52, Number 2 (2011), 173-185.

Dates
First available in Project Euclid: 28 April 2011

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1303995713

Digital Object Identifier
doi:10.1215/00294527-1306181

Zentralblatt MATH identifier
05903677

Mathematical Reviews number (MathSciNet)
MR2794650

Subjects
Primary: 03D32: Algorithmic randomness and dimension [See also 68Q30]

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

Citation

Franklin, Johanna N.Y.; Stephan, Frank. Van Lambalgen's Theorem and High Degrees. Notre Dame Journal of Formal Logic 52 (2011), no. 2, 173--185. doi:10.1215/00294527-1306181. http://projecteuclid.org/euclid.ndjfl/1303995713.


Export citation