Translator Disclaimer
March 2009 From index sets to randomness in ∅n: random reals and possibly infinite computations. Part II
Verónica Becher, Serge Grigorieff
J. Symbolic Logic 74(1): 124-156 (March 2009). DOI: 10.2178/jsl/1231082305

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.

Citation

Download Citation

Verónica Becher. Serge Grigorieff. "From index sets to randomness in ∅n: random reals and possibly infinite computations. Part II." J. Symbolic Logic 74 (1) 124 - 156, March 2009. https://doi.org/10.2178/jsl/1231082305

Information

Published: March 2009
First available in Project Euclid: 4 January 2009

zbMATH: 1163.03023
MathSciNet: MR2499423
Digital Object Identifier: 10.2178/jsl/1231082305

Rights: Copyright © 2009 Association for Symbolic Logic

JOURNAL ARTICLE
33 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.74 • No. 1 • March 2009
Back to Top