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### Paper:

TR10-150 | 19th September 2010 03:21

#### A strong law of computationally weak subsets

TR10-150
Authors: Bjørn Kjos-Hanssen
Publication: 1st October 2010 11:06
We show that in the setting of fair-coin measure on the power set of the natural numbers, each sufficiently random set has an infinite subset that computes no random set. That is, there is an almost sure event $\mathcal A$ such that if $X\in\mathcal A$ then $X$ has an infinite subset $Y$ such that no element of $\mathcal A$ is Turing computable from $Y$.