English

A strong law of computationally weak subsets

Logic 2014-08-12 v1

Abstract

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 A\mathcal A such that if XAX\in\mathcal A then XX has an infinite subset YY such that no element of A\mathcal A is Turing computable from YY.

Keywords

Cite

@article{arxiv.1408.1967,
  title  = {A strong law of computationally weak subsets},
  author = {Bjørn Kjos-Hanssen},
  journal= {arXiv preprint arXiv:1408.1967},
  year   = {2014}
}
R2 v1 2026-06-22T05:23:39.684Z