Productivity of maximal eventually different families

Lukas Schembecker

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arXiv · 2606.18137

Productivity of maximal eventually different families

Lukas Schembecker

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Abstract

A maximal eventually different family is called $n$-productive if the product family $\mathcal{F}^n$ is still maximal. We construct closed $n$-productive families separating these strengthenings of maximality at every $n \geq 1$. Furthermore, we show how to force and construct an even stronger type of $\mathcal{I}_0$-productive family and discuss the relation of productivity to Van Douwen families.

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Lukas Schembecker. 2026-06-16. Productivity of maximal eventually different families. https://arxiv.org/abs/2606.18137

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