Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Houérou, Quentin Le, Patey, Ludovic
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7128470914
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