Using random sets as oracles
Denis R. Hirschfeldt, André Nies, Frank Stephan · Journal of the London Mathematical Society · 2007
Let R be a notion of algorithmic randomness for individual subsets of ℕ. A set B is a base for R randomness if there is a Z ⩾T B such that Z is R random relative to B. We show that the bases for 1-randomness are exactly the K-trivial sets, and discuss several consequences of this result. On the other hand, the bases for computable randomness include every Δ20 set that is not diagonally noncomputable, but no set of PA-degree. As a consequence, an n-c.e. set is a base for computable randomness if and only if it is Turing incomplete.