Superhighness

Notre Dame Journal of Formal Logic 50 (4):445-452 (2009)
Abstract
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
Keywords Turing degrees   highness and lowness notions   algorithmic randomness   truth-table degrees
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