A generalization of Chaitin's halting probability $\Omega$ and halting self-similar sets

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A Generalization of Chaitin's Halting Probability \Omega and Halting Self-Similar Sets

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As a natural example of a 1-random real, Chaitin proposed the halting probability Ω of a universal prefix-free machine. We can relativize this example by considering a universal prefix-free oracle machine U . Let ΩU be the halting probability of U A; this gives a natural uniform way of producing an A-random real for every A ∈ 2ω . It is this operator which is our primary object of study. We can...

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ژورنال

عنوان ژورنال: Hokkaido Mathematical Journal

سال: 2002

ISSN: 0385-4035

DOI: 10.14492/hokmj/1350911778