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September 2004 Every 2-random real is Kolmogorov random
Joseph S. Miller
J. Symbolic Logic 69(3): 907-913 (September 2004). DOI: 10.2178/jsl/1096901774

Abstract

We study reals with infinitely many incompressible prefixes. Call A∈ 2ω Kolmogorov random if (∃n) C(A↾ n)> n-(1), where C denotes plain Kolmogorov complexity. This property was suggested by Loveland and studied by Martin-Löf, Schnorr and Solovay. We prove that 2-random reals are Kolmogorov random. Together with the converse—proved by Nies, Stephan and Terwijn [NST]—this provides a natural characterization of 2-randomness in terms of plain complexity. We finish with a related characterization of 2-randomness.

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Joseph S. Miller. "Every 2-random real is Kolmogorov random." J. Symbolic Logic 69 (3) 907 - 913, September 2004. https://doi.org/10.2178/jsl/1096901774

Information

Published: September 2004
First available in Project Euclid: 4 October 2004

zbMATH: 1090.03012
MathSciNet: MR2078929
Digital Object Identifier: 10.2178/jsl/1096901774

Rights: Copyright © 2004 Association for Symbolic Logic

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Vol.69 • No. 3 • September 2004
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