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arXiv · 2305.10529

The descriptive complexity of the set of Poisson generic numbers

Verónica Becher·Stephen Jackson·Dominik Kwietniak·Bill Mance
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Abstract

Let $b\ge 2$ be an integer. We show that the set of real numbers that are Poisson generic in base $b$ is $\boldsymbol{\Pi}^0_3$-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 $\boldsymbol{\Pi}^0_3$ sets. We also show that the effective versions of these results hold in the effective Borel hierarchy.

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Verónica Becher, Stephen Jackson, Dominik Kwietniak, Bill Mance. 2023-05-17. The descriptive complexity of the set of Poisson generic numbers. https://arxiv.org/abs/2305.10529

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