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Another Example of Higher Order Randomness
 FUNDAMENTA INFORMATICAE
, 2002
"... We consider the notion of algorithmic randomness relative to an oracle. We prove that the probability # that a program for infinite computations (a program that never halts) outputs a cofinite set is random in the second jump of the halting problem. Indeed, we prove that # is exactly as random as ..."
Abstract

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We consider the notion of algorithmic randomness relative to an oracle. We prove that the probability # that a program for infinite computations (a program that never halts) outputs a cofinite set is random in the second jump of the halting problem. Indeed, we prove that # is exactly as random as the halting probability of a universal machine equipped with an oracle for the second jump of the halting problem, in spite of the fact that # is defined without considering oracles.