Avoid Schnorr randomness

TL;DR

This paper demonstrates that for any finite partition of natural numbers, there exists an infinite subset that cannot compute a Schnorr random real, addressing open questions in algorithmic randomness and computability theory.

Contribution

It proves the existence of non-computing infinite subsets for any finite partition, advancing understanding of Schnorr randomness and computability.

Findings

Existence of infinite subsets avoiding Schnorr randomness in any finite partition

Answers to open questions by Brendle et al.

Strengthening of a result by Khan and Miller.

Abstract

We prove that every finite partition of $\omega$ admit an infinite subset that does not compute a Schnorr random real. We use this result to answer two questions of Brendle, Brooke-Taylor, Ng and Nies and strength a result of Khan and Miller.