Lowness Properties of Reals and Hyper-Immunity
Abstract Ambos-Spies and Kucera [1, Problem 4.5] asked if there is a non-computable set A which is low for the computably random reals. We show that no such A is of hyper-immune degree. Thus, each g ≤ T A is dominated by a computable function. Ambos-Spies and Kucera [1, problem 4.8] also asked if every S-low set is S 0 -low. We give a partial solution to this problem, showing that no S -low set is of hyper-immune degree.