Notre Dame Journal of Formal Logic 51 (3):337-349 (2010)

Abstract
Van Lambalgen's Theorem plays an important role in algorithmic randomness, especially when studying relative randomness. In this paper we extend van Lambalgen's Theorem by considering the join of infinitely many reals which are random relative to each other. In addition, we study computability of the reals in the range of Omega operators. It is known that $\Omega^{\phi'}$ is high. We extend this result to that $\Omega^{\phi^{(n)}}$ is $\textrm{high}_n$ . We also prove that there exists A such that, for each n , the real $\Omega^A_M$ is $\textrm{high}_n$ for some universal Turing machine M by using the extended van Lambalgen's Theorem
Keywords van Lambalgen's Theorem   martingale   high   Omega operator
Categories (categorize this paper)
DOI 10.1215/00294527-2010-020
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 69,043
Through your library

References found in this work BETA

Add more references

Citations of this work BETA

Characterizing Strong Randomness Via Martin-Löf Randomness.Liang Yu - 2012 - Annals of Pure and Applied Logic 163 (3):214-224.

Add more citations

Similar books and articles

Every 2-Random Real is Kolmogorov Random.Joseph S. Miller - 2004 - Journal of Symbolic Logic 69 (3):907-913.
Schnorr Randomness.Rodney G. Downey & Evan J. Griffiths - 2004 - Journal of Symbolic Logic 69 (2):533 - 554.
Subclasses of the Weakly Random Reals.Johanna N. Y. Franklin - 2010 - Notre Dame Journal of Formal Logic 51 (4):417-426.
Relative Randomness and Real Closed Fields.Alexander Raichev - 2005 - Journal of Symbolic Logic 70 (1):319 - 330.
Relative Randomness and Cardinality.George Barmpalias - 2010 - Notre Dame Journal of Formal Logic 51 (2):195-205.
Van Lambalgen's Theorem and High Degrees.Johanna N. Y. Franklin & Frank Stephan - 2011 - Notre Dame Journal of Formal Logic 52 (2):173-185.

Analytics

Added to PP index
2010-08-19

Total views
37 ( #304,725 of 2,498,570 )

Recent downloads (6 months)
1 ( #426,098 of 2,498,570 )

How can I increase my downloads?

Downloads

My notes