Normal numbers and limit computable Cantor series
Logic
2017-10-18 v1
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 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.
Cite
@article{arxiv.1404.2178,
title = {Normal numbers and limit computable Cantor series},
author = {Achilles A. Beros and Konstantinos A. Beros},
journal= {arXiv preprint arXiv:1404.2178},
year = {2017}
}
Comments
5 pages