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Normal numbers and the Borel hierarchy

Verónica Becher; Pablo Ariel Heiber; Theodore A. Slaman — 2014

Fundamenta Mathematicae

We show that the set of absolutely normal numbers is 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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