Superhighness
  We prove that superhigh sets can be jump traceable, answering a question of Cole and Simpson. On the other hand, we show that such sets cannot be weakly 2-random. We also study the class superhigh$^\Diamond$, and show that it contains some, but not all, of the noncomputable $K$-trivial sets. 
Andr\'e Nies and Bj{\o}rn Kjos-Hanssen
math.LO