Normal Numbers and the Borel Hierarchy

2013/11/02 by Becher, Verónica, Heiber, Pablo Ariel, Slaman, Theodore A. · 1 citation
#FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic in Computer Science (cs.LO)

paper · doi:10.48550/arxiv.1311.0335

Abstract

We show that the set of absolutely normal numbers is \mathbf Π⁰₃-complete in the Borel hierarchy of subsets of real numbers. Similarly, the set of absolutely normal numbers is Π⁰₃-complete in the effective Borel hierarchy.

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