Normal numbers and the Borel hierarchy
Volume 226 / 2014
Fundamenta Mathematicae 226 (2014), 63-77
MSC: 11U99, 03E15, 68W99.
DOI: 10.4064/fm226-1-4
Abstract
We show that the set of absolutely normal numbers is $\mathbf \Pi ^0_3$-complete in the Borel hierarchy of subsets of real numbers. Similarly, the set of absolutely normal numbers is $\Pi ^0_3$-complete in the effective Borel hierarchy.
