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arXiv · 2510.07222

Coanalytic families of functions

Julia Millhouse·Lukas Schembecker
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Abstract

For Van Douwen families, maximal families of eventually different permutations and maximal ideal independent families we show that the existence of a $\Sigma^1_2$ family implies the existence of a $\Pi^1_1$ family of the same size. We also prove a similar, but slightly weaker result for generating sets of cofinitary groups.

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Julia Millhouse, Lukas Schembecker. 2025-10-08. Coanalytic families of functions. https://arxiv.org/abs/2510.07222

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