Avoid Schnorr randomness

2019/12/19 by Liu, Lu
#68Q30 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1912.09052

Abstract

We prove that every finite partition of ω 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.

Related

• Uniform distribution and algorithmic randomness
• Schnorr randomness for noncomputable measures
• A generalization of Levin-Schnorr's theorem
• Combinatorial and number-theoretic properties of generic reals
• The uses of random partitions