Translator Disclaimer
2010 An Extension of van Lambalgen's Theorem to Infinitely Many Relative 1-Random Reals
Kenshi Miyabe
Notre Dame J. Formal Logic 51(3): 337-349 (2010). DOI: 10.1215/00294527-2010-020

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 Ω ϕ is high. We extend this result to that Ω ϕ ( n ) is high n . We also prove that there exists A such that, for each n, the real Ω M A is high n for some universal Turing machine M by using the extended van Lambalgen's Theorem.

Citation

Download Citation

Kenshi Miyabe. "An Extension of van Lambalgen's Theorem to Infinitely Many Relative 1-Random Reals." Notre Dame J. Formal Logic 51 (3) 337 - 349, 2010. https://doi.org/10.1215/00294527-2010-020

Information

Published: 2010
First available in Project Euclid: 18 August 2010

zbMATH: 1208.03045
MathSciNet: MR2675686
Digital Object Identifier: 10.1215/00294527-2010-020

Subjects:
Primary: 03D32
Secondary: 03D25

Rights: Copyright © 2010 University of Notre Dame

JOURNAL ARTICLE
13 PAGES


SHARE
Vol.51 • No. 3 • 2010
Back to Top