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December 2003 The Kolmogorov-Loveland stochastic sequences are not closed under selecting subsequences
Wolfgang Merkle
J. Symbolic Logic 68(4): 1362-1376 (December 2003). DOI: 10.2178/jsl/1067620192

Abstract

It is shown that the class of Kolmogorov-Loveland stochastic sequences is not closed under selecting subsequences by monotonic computable selection rules. This result gives a strong negative answer to the question whether the Kolmogorov-Loveland stochastic sequences are closed under selecting sequences by Kolmogorov-Loveland selection rules, i.e., by not necessarily monotonic, partial computable selection rules. The following previously known results are obtained as corollaries. The Mises-Wald-Church stochastic sequences are not closed under computable permutations, hence in particular they form a strict superclass of the class of Kolmogorov-Loveland stochastic sequences. The Kolmogorov-Loveland selection rules are not closed under composition.

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Wolfgang Merkle. "The Kolmogorov-Loveland stochastic sequences are not closed under selecting subsequences." J. Symbolic Logic 68 (4) 1362 - 1376, December 2003. https://doi.org/10.2178/jsl/1067620192

Information

Published: December 2003
First available in Project Euclid: 31 October 2003

zbMATH: 1065.03024
MathSciNet: MR2017360
Digital Object Identifier: 10.2178/jsl/1067620192

Rights: Copyright © 2003 Association for Symbolic Logic

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Vol.68 • No. 4 • December 2003
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