Normal numbers and limit computable Cantor series
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 Delta0n+1 basic sequence with respect to which no Delta0n 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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