Normal Numbers and Limit Computable Cantor Series

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Notre Dame Journal of Formal Logic 58 (2):215-220 (2017)
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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.

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10.1215/00294527-2017-0004

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