Infinite subsets of random sets of integers

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.

Cited by in corpus (3)

• Martin-Löf randomness and Galton-Watson processes
• A strong law of computationally weak subsets
• Partition genericity and pigeonhole basis theorems