Maximal eventually different families for uniformly weak Ramsey ideals

2024/12/25 by Jialiang He, He, Jialiang, Jintao Luo +5
Mathematics · #Advanced Topology and Set Theory #Rings, Modules, and Algebras #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2412.18987

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 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_σ ideals and Fubini products fin^α with α<ω₁.

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