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September 2004 On the construction of effectively random sets
Wolfgang Merkle, Nenad Mihailović
J. Symbolic Logic 69(3): 862-878 (September 2004). DOI: 10.2178/jsl/1096901772

Abstract

We present a comparatively simple way to construct Martin-Löf random and rec-random sets with certain additional properties, which works by diagonalizing against appropriate martingales. Reviewing the result of Gács and Kučera, for any given set X we construct a Martin-Löf random set from which X can be decoded effectively. By a variant of the basic construction we obtain a rec-random set that is weak truth-table autoreducible and we observe that there are Martin-Löf random sets that are computably enumerable self-reducible. The two latter results complement the known facts that no rec-random set is truth-table autoreducible and that no Martin-Löf random set is Turing-autoreducible [ebert-merkle-vollmer-2002,trakhtenbrot-1970].

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Wolfgang Merkle. Nenad Mihailović. "On the construction of effectively random sets." J. Symbolic Logic 69 (3) 862 - 878, September 2004. https://doi.org/10.2178/jsl/1096901772

Information

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

zbMATH: 1090.03011
MathSciNet: MR2078927
Digital Object Identifier: 10.2178/jsl/1096901772

Rights: Copyright © 2004 Association for Symbolic Logic

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Vol.69 • No. 3 • September 2004
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