Mathematical Research Letters

Volume 16 (2009)

Number 1

Infinite Subsets of Random Sets of Integers

Pages: 103 – 110

DOI: http://dx.doi.org/10.4310/MRL.2009.v16.n1.a10

Author

Bjørn Kjos-Hanssen (University of Hawaii)

Abstract

There is an infinite subset of a Martin-Löf random set of integers that does not compute any Martin-Löf random set of integers. To prove this, we show that each real of positive effective Hausdorff dimension computes an infinite subset of a Martin-Löf random set of integers, and apply a result of Miller.

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