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arXiv · 2412.18987

Maximal eventually different families for uniformly weak Ramsey ideals

Jialiang He·Jintao Luo·David Schrittesser·Hang Zhang
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Abstract

We study $\mathcal I$-maximal eventually different families of functions from the set of natural numbers into itself where $\mathcal I$ is an arbitrary ideal on the set of natural numbers that includes the ideal of all finite sets $\mathrm{fin}$. We introduce the class of uniformly weak Ramsey ideals and prove that there exists a closed $\mathcal I$-maximal eventually different family if $\mathcal I$ belongs to this class; this is the case for arbitrary $F_\sigma$ ideals and Fubini products $\mathrm{fin}^{\alpha}$ with $\alpha<\omega_1$.

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Jialiang He, Jintao Luo, David Schrittesser, Hang Zhang. 2024-12-25. Maximal eventually different families for uniformly weak Ramsey ideals. https://arxiv.org/abs/2412.18987

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