Van Lambalgen's Theorem and High Degrees

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

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
Keywords van Lambalgen's Theorem   Schnorr randomness   recursive randomness   Kurtz randomness
Categories (categorize this paper)
DOI 10.1215/00294527-1306181
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 39,545
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

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 index
2011-04-29

Total views
663 ( #4,207 of 2,325,369 )

Recent downloads (6 months)
12 ( #78,606 of 2,325,369 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature