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2017 Normal Numbers and Limit Computable Cantor Series
Achilles Beros, Konstantinos Beros
Notre Dame J. Formal Logic 58(2): 215-220 (2017). DOI: 10.1215/00294527-2017-0004

Abstract

Given any oracle, A, we construct a basic sequence Q, computable in the jump of A, such that no A-computable real is Q-distribution-normal. A corollary to this is that there is a Δn+10 basic sequence with respect to which no Δn0 real is distribution-normal. As a special case, there is a limit computable sequence relative to which no computable real is distribution-normal.

Citation

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Achilles Beros. Konstantinos Beros. "Normal Numbers and Limit Computable Cantor Series." Notre Dame J. Formal Logic 58 (2) 215 - 220, 2017. https://doi.org/10.1215/00294527-2017-0004

Information

Received: 8 April 2014; Accepted: 21 November 2014; Published: 2017
First available in Project Euclid: 22 March 2017

zbMATH: 06751299
MathSciNet: MR3634977
Digital Object Identifier: 10.1215/00294527-2017-0004

Subjects:
Primary: 03D28
Secondary: 03D80

Rights: Copyright © 2017 University of Notre Dame

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Vol.58 • No. 2 • 2017
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