Normal Numbers and Limit Computable Cantor Series
Achilles A. Beros, Konstantinos A. Beros · Notre Dame Journal of Formal Logic · 2017
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.