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  1.  23
    Kolmogorov–Loveland Randomness and Stochasticity.Wolfgang Merkle, Joseph S. Miller, André Nies, Jan Reimann & Frank Stephan - 2006 - Annals of Pure and Applied Logic 138 (1):183-210.
    An infinite binary sequence X is Kolmogorov–Loveland random if there is no computable non-monotonic betting strategy that succeeds on X in the sense of having an unbounded gain in the limit while betting successively on bits of X. A sequence X is KL-stochastic if there is no computable non-monotonic selection rule that selects from X an infinite, biased sequence.One of the major open problems in the field of effective randomness is whether Martin-Löf randomness is the same as KL-randomness. Our first (...)
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  2.  12
    Effectively Closed Sets of Measures and Randomness.Jan Reimann - 2008 - Annals of Pure and Applied Logic 156 (1):170-182.
    We show that if a real x2ω is strongly Hausdorff -random, where h is a dimension function corresponding to a convex order, then it is also random for a continuous probability measure μ such that the μ-measure of the basic open cylinders shrinks according to h. The proof uses a new method to construct measures, based on effective continuous transformations and a basis theorem for -classes applied to closed sets of probability measures. We use the main result to derive a (...)
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  3.  11
    Independence, Relative Randomness, and PA Degrees.Adam R. Day & Jan Reimann - 2014 - Notre Dame Journal of Formal Logic 55 (1):1-10.
  4.  26
    Reviewed Work(S): Some Theorems on the Algorithmic Approach to Probability Theory and Information Theory (1971 Dissertation Directed by A. N. Kolmogorov). Annals of Pure and Applied Logic, Vol. 162 by L. A. Levin. [REVIEW]Jan Reimann - forthcoming - Association for Symbolic Logic: The Bulletin of Symbolic Logic.
    Review by: Jan Reimann The Bulletin of Symbolic Logic, Volume 19, Issue 3, Page 397-399, September 2013.
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  5.  19
    Conference on Computability, Complexity and Randomness.Verónica Becher, C. T. Chong, Rod Downey, Noam Greenberg, Antonin Kucera, Bjørn Kjos-Hanssen, Steffen Lempp, Antonio Montalbán, Jan Reimann & Stephen Simpson - 2008 - Bulletin of Symbolic Logic 14 (4):548-549.
  6.  8
    Córdoba, Argentina September 20–24, 2004.Joos Heintz, Antonın Kucera, Joseph Miller, André Nies, Jan Reimann, Theodore Slaman, Diego Vaggione, Paul Vitányi & Verónica Becher - 2005 - Bulletin of Symbolic Logic 11 (4).
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  7.  2
    L. A. Levin. Some Theorems on the Algorithmic Approach to Probability Theory and Information Theory . Annals of Pure and Applied Logic, Vol. 162 , Pp. 224–235. [REVIEW]Jan Reimann - 2013 - Bulletin of Symbolic Logic 19 (3):397-399.
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