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arXiv · 2606.05790

Strong colorings based on oscillations

Stevo Todorcevic·Jing Zhang
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Abstract

We show that for any uncountable cardinal $κ$, there is a coloring $c: [κ]^2\to ω$ such that $c''A \otimes B = ω$ for any $A, B\subseteq κ$ of order type $ω_1$ that are stationary in their common supremum. In particular, the stationary version of Erdős-Rado theorem and the higher dimensional Friedman's property are both inconsistent. We demonstrate that the theorem is optimal in various ways.

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Stevo Todorcevic, Jing Zhang. 2026-06-04. Strong colorings based on oscillations. https://arxiv.org/abs/2606.05790

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