Avoid Schnorr randomness

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.

References in corpus (2)

• Kolmogorov complexity and the Recursion Theorem
• The Strength of Some Combinatorial Principles Related to Ramsey's Theorem for Pairs