Some complexity results in the theory of normal numbers

Dylan Airey, Bill Mance, Steve Jackson

Let $\mathcal{N}(b)$ be the set of real numbers which are normal to base $b$. A well-known result of H. Ki and T. Linton is that $\mathcal{N}(b)$ is ${\mathbf{\Pi }}_3^0$-complete. We…