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 and show that it contains some, but not all, of the noncomputable K-trivial sets.
"Superhighness." Notre Dame J. Formal Logic 50 (4) 445 - 452, 2009. https://doi.org/10.1215/00294527-2009-020