Journal of Symbolic Logic

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

Verónica Becher and Serge Grigorieff

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 4 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1231082305

Digital Object Identifier
doi:10.2178/jsl/1231082305

Mathematical Reviews number (MathSciNet)
MR2499423

Zentralblatt MATH identifier
1163.03023

Citation

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. https://projecteuclid.org/euclid.jsl/1231082305


Export citation