From index sets to randomness in ∅n: random reals and possibly infinite computations part II
Verónica Becher, Serge Grigorieff · Journal of Symbolic Logic · 2009
Abstract We obtain a large class of significant examples ofn-random reals (i.e., Martin-Löf random in oracle ∅(n−1)) à la Chaitin. Any such real is defined as the probability that a universal monotone Turing machine performing possibly infinite computations on infinite (resp. finite large enough, resp. finite self-delimited) inputs produces an output in a given set . In particular, we develop methods to transfer many-one completeness results of index sets ton-randomness of associated probabilities.