We say that A ≤LR B if every B-random set is A-random with respect to Martin-Löf randomness. We study this reducibility and its interactions with the Turing reducibility, Π1 classes, hyperimmunity and other recursion theoretic notions. A natural variant of the Turing reducibility from the point of view of Martin-Löf randomness is the LR reducibility which was introduced in [12]. We say that A ≤...

The high/low hierarchy respects the ordering of degrees, and so we can expect to find properties of order which are possessed by all degrees in a given hierarchy class. Such properties can also be found for classes of the generalized high/low hierarchy even though that hierarchy does not respect the ordering of the degrees. For example, Jockusch and Posner [4], extending a result of Cooper [l],...