Journal of Symbolic Logic

From index sets to randomness in ∅n: random reals and possibly infinite computations. Part II

Verónica Becher and Serge Grigorieff

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We obtain a large class of significant examples of n-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 𝒪⊆ 𝔓(ℕ). In particular, we develop methods to transfer Σ0n or Π0n many-one completeness results of index sets to n-randomness of associated probabilities.

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J. Symbolic Logic, Volume 74, Issue 1 (2009), 124-156.

First available in Project Euclid: 4 January 2009

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Becher, Verónica; Grigorieff, Serge. From index sets to randomness in ∅ n : random reals and possibly infinite computations. Part II. J. Symbolic Logic 74 (2009), no. 1, 124--156. doi:10.2178/jsl/1231082305.

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