Partition theorems for Ketonen-Solovay largeness: Hardy-like version

Quentin Le Houérou; Ludovic Patey

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arXiv · 2602.08778

Partition theorems for Ketonen-Solovay largeness: Hardy-like version

Quentin Le Houérou·Ludovic Patey

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Abstract

We develop the framework of $α$-largeness introduced by Ketonen and Solovay, by proving a partition theorem for $α$-large sets with $α< ε_0$ which generalizes theorems from Ketonen and Solovay and from Bigorajska and Kotlarski. We also prove that for every $ω^{nk+3}$-large set $X$ with $\min X \geq 18$, every coloring $f : [X]^2 \to k$ admits an $ω^n$-large $f$-homogeneous subset. This bound is tight, up to an additive constant.

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BibTeX RIS

Quentin Le Houérou, Ludovic Patey. 2026-08-24. Partition theorems for Ketonen-Solovay largeness: Hardy-like version. https://arxiv.org/abs/2602.08778

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