Higher Kurtz randomness

摘要

A real x is δ~1_1-Kurtz random (Π~1_1-Kurtz random) if it is in no closed null δ~1_1 set (Π~1_1 set). We show that there is a cone of Π~1_1-Kurtz random hyperdegrees. We characterize lowness for δ~1_1-Kurtz randomness as being δ~1_1-dominated and δ~1_1-semi-traceable.