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  1. Cone Avoidance and Randomness Preservation.Stephen G. Simpson & Frank Stephan - 2015 - Annals of Pure and Applied Logic 166 (6):713-728.
  • Randomness for Computable Measures and Initial Segment Complexity.Rupert Hölzl & Christopher P. Porter - 2017 - Annals of Pure and Applied Logic 168 (4):860-886.
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  • On Effectively Closed Sets of Effective Strong Measure Zero.Kojiro Higuchi & Takayuki Kihara - 2014 - Annals of Pure and Applied Logic 165 (9):1445-1469.
    The strong measure zero sets of reals have been widely studied in the context of set theory of the real line. The notion of strong measure zero is straightforwardly effectivized. A set of reals is said to be of effective strong measure zero if for any computable sequence {εn}n∈N{εn}n∈N of positive rationals, a sequence of intervals InIn of diameter εnεn covers the set. We observe that a set is of effective strong measure zero if and only if it is of (...)
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  • The Axiomatic Power of Kolmogorov Complexity.Laurent Bienvenu, Andrei Romashchenko, Alexander Shen, Antoine Taveneaux & Stijn Vermeeren - 2014 - Annals of Pure and Applied Logic 165 (9):1380-1402.
    The famous Gödel incompleteness theorem states that for every consistent, recursive, and sufficiently rich formal theory T there exist true statements that are unprovable in T . Such statements would be natural candidates for being added as axioms, but how can we obtain them? One classical approach is to add to some theory T an axiom that claims the consistency of T . In this paper we discuss another approach motivated by Chaitin's version of Gödel's theorem where axioms claiming the (...)
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