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Every 2-random real is Kolmogorov random

Published online by Cambridge University Press:  12 March 2014

Joseph S. Miller
Joseph S. Miller*
Affiliation:
School of Mathematical and Computing Sciences, Victoria University, P.O. Box 600 Wellington, New Zealand, E-mail: Joe.Miller@mcs.vuw.ac.nz
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Abstract.

We study reals with infinitely many incompressible prefixes. Call A ∈ 2ωKolmogorov random if . 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 [11]—this provides a natural characterization of 2-randomness in terms of plain complexity. We finish with a related characterization of 2-randomness.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 69 , Issue 3 , September 2004 , pp. 907 - 913
Copyright
Copyright © Association for Symbolic Logic 2004

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References

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