Van Lambalgen's theorem and high degrees
type: Item
instance of: scholarly article
title: Van Lambalgen's theorem and high degrees
zbMATH Open document ID: 1223.03024
DOI: 10.1215/00294527-1306181
author: Johanna N. Y. Franklin
author: Frank Stephan
published in: Notre Dame Journal of Formal Logic
publication date: 2011-06-03T00:00:00Z
review text: In the paper under review, the authors investigate when and where van Lambalgen's theorem fails respectively holds. They prove that: {\parindent5.5mm \begin{itemize}\item[1)] Each high degree contains a recursively random real so that van Lambalgen's theorem fails; \item[2)] Each hyperimmune degree contains a Kurtz random real so that van Lambalgen's theorem fails; \item[3)] There is a recursively random real that is not Martin-Löf random and satisfies van Lambalgen's theorem for recursive, Schnorr and Kurtz randomness. \end{itemize}}
reviewed by: Liang Yu
Mathematics Subject Classification ID: 03D32
zbMATH DE Number: 5903677
zbMATH Keywords: van Lambalgen's theorem
zbMATH Keywords: Schnorr randomness
zbMATH Keywords: recursive randomness
zbMATH Keywords: Kurtz randomness
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/00294527-1306181
OpenAlex ID: W1995163461
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description: scientific article; zbMATH DE number 5903677