Van Lambalgen's Theorem and High Degrees

Notre Dame Journal of Formal Logic 52 (2):173-185 (2011)
  Copy   BIBTEX

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

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,221

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Schnorr Randomness.Rodney G. Downey & Evan J. Griffiths - 2004 - Journal of Symbolic Logic 69 (2):533 - 554.
The axiomatization of randomness.Michiel van Lambalgen - 1990 - Journal of Symbolic Logic 55 (3):1143-1167.
Independence, randomness and the axiom of choice.Michiel van Lambalgen - 1992 - Journal of Symbolic Logic 57 (4):1274-1304.
Von Mises' definition of random sequences reconsidered.Michiel van Lambalgen - 1987 - Journal of Symbolic Logic 52 (3):725-755.
Formal models for real people.Michiel van Lambalgen & Marian Counihan - 2008 - Journal of Logic, Language and Information 17 (4):385-389.

Analytics

Added to PP
2011-04-29

Downloads
691 (#21,249)

6 months
2 (#658,848)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

An application of recursion theory to analysis.Liang Yu - 2020 - Bulletin of Symbolic Logic 26 (1):15-25.

Add more citations

References found in this work

The axiomatization of randomness.Michiel van Lambalgen - 1990 - Journal of Symbolic Logic 55 (3):1143-1167.
Minimal degrees and the jump operator.S. B. Cooper - 1973 - Journal of Symbolic Logic 38 (2):249-271.
Uniform Almost Everywhere Domination.Peter Cholak, Noam Greenberg & Joseph S. Miller - 2006 - Journal of Symbolic Logic 71 (3):1057 - 1072.

View all 9 references / Add more references