Notre Dame Journal of Formal Logic

Normal Numbers and Limit Computable Cantor Series

Achilles Beros and Konstantinos Beros

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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 $\Delta^{0}_{n+1}$ basic sequence with respect to which no $\Delta^{0}_{n}$ real is distribution-normal. As a special case, there is a limit computable sequence relative to which no computable real is distribution-normal.

Article information

Notre Dame J. Formal Logic Volume 58, Number 2 (2017), 215-220.

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

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Digital Object Identifier

Primary: 03D28: Other Turing degree structures
Secondary: 03D80: Applications of computability and recursion theory

computability theory recursion theory Turing degrees number theory normal numbers Cantor series expansions basic series


Beros, Achilles; Beros, Konstantinos. Normal Numbers and Limit Computable Cantor Series. Notre Dame J. Formal Logic 58 (2017), no. 2, 215--220. doi:10.1215/00294527-2017-0004.

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