Higher Kurtz randomness
  A real $x$ is $\Delta^1_1$-Kurtz random ($\Pi^1_1$-Kurtz random) if it is in no closed null $\Delta^1_1$ set ($\Pi^1_1$ set). We show that there is a cone of $\Pi^1_1$-Kurtz random hyperdegrees. We characterize lowness for $\Delta^1_1$-Kurtz randomness as being $\Delta^1_1$-dominated and $\Delta^1_1$-semi-traceable. 
Bj{\o}rn Kjos-Hanssen, Andr\'e Nies, Frank Stephan, and Liang Yu
math.LO