Partition theorems for Ketonen-Solovay largeness
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We develop the framework of \(\alpha\)-largeness introduced by Ketonen and Solovay, by proving a partition theorem for \(\alpha\)-large sets with \(\alpha < \epsilon_0\) which generalizes theorems from Ketonen and Solovay and from Bigorajska and Kotlarski. We also prove that for every \(\omega^{nk+3}\)-large set~\(X\) with \(\min X \geq 18\), every coloring \(f : [X]^2 \to k\) admits an \(\omega^n\)-large \(f\)-homogeneous subset. This bound is tight, up to an additive constant.
Recommended citation: Q. Le Houérou and L. Patey (2026). "Partition theorems for Ketonen-Solovay largeness."
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