Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 51, Number 3 (2010), 337-349.
An Extension of van Lambalgen's Theorem to Infinitely Many Relative 1-Random Reals
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 is high. We extend this result to that is . We also prove that there exists A such that, for each n, the real is for some universal Turing machine M by using the extended van Lambalgen's Theorem.
Notre Dame J. Formal Logic Volume 51, Number 3 (2010), 337-349.
First available in Project Euclid: 18 August 2010
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03D32: Algorithmic randomness and dimension [See also 68Q30]
Secondary: 03D25: Recursively (computably) enumerable sets and degrees
Miyabe, Kenshi. An Extension of van Lambalgen's Theorem to Infinitely Many Relative 1-Random Reals. Notre Dame J. Formal Logic 51 (2010), no. 3, 337--349. doi:10.1215/00294527-2010-020. https://projecteuclid.org/euclid.ndjfl/1282137986