Structural Infinite-Exponent Partition Relations and Weak Choice Principles

Lyra A. Gardiner; Jonathan Schilhan

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arXiv · 2605.21259

Structural Infinite-Exponent Partition Relations and Weak Choice Principles

Lyra A. Gardiner·Jonathan Schilhan

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Abstract

We investigate infinite-exponent partition relations on arbitrary relational structures, with a focus on linear orders and graphs. Any such relation contradicts the Axiom of Choice. We show that there are some such relations which are consistent with ZF which imply the failure not just of Choice but also of the Kinna-Wagner Selection Principle KWP$_1$ and the Ordering Principle O.

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Lyra A. Gardiner, Jonathan Schilhan. 2026-05-20. Structural Infinite-Exponent Partition Relations and Weak Choice Principles. https://arxiv.org/abs/2605.21259

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