The axiomatization of randomness

Journal of Symbolic Logic 55 (3):1143-1167 (1990)
Abstract
We present a faithful axiomatization of von Mises' notion of a random sequence, using an abstract independence relation. A byproduct is a quantifier elimination theorem for Friedman's "almost all" quantifier in terms of this independence relation
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DOI 10.2307/2274480
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Randomness and Computability: Open Questions.Joseph S. Miller & André Nies - 2006 - Bulletin of Symbolic Logic 12 (3):390-410.
Calibrating Randomness.Rod Downey, Denis R. Hirschfeldt, André Nies & Sebastiaan A. Terwijn - 2006 - Bulletin of Symbolic Logic 12 (3):411-491.
On Relative Randomness.Antonín Kučera - 1993 - Annals of Pure and Applied Logic 63 (1):61-67.
Probabilistic Issues in Statistical Mechanics.Gérard G. Emch - 2005 - Studies in History and Philosophy of Science Part B 36 (2):303-322.

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