The descriptive complexity of the set of Poisson generic numbers

2023/05/17 by Becher, Verónica, Jackson, Stephen, Kwietniak, Dominik +1 · 1 citation
#FOS: Mathematics #Logic (math.LO) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2305.10529

Abstract

Let b≥ 2 be an integer. We show that the set of real numbers that are Poisson generic in base b is \boldsymbolΠ⁰₃-complete in the Borel hierarchy of subsets of the real line. Furthermore, the set of real numbers that are Borel normal in base b and not Poisson generic in base b is complete for the class given by the differences between \boldsymbolΠ⁰₃ sets. We also show that the effective versions of these results hold in the effective Borel hierarchy.

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