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arXiv · 2507.12361

Infinite-Exponent Partition Relations on the Real Line

Lyra A. Gardiner
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Abstract

We extend the theory of infinite-exponent partition relations to arbitrary linear order types, with a particular focus on the real number line. We give a complete classification of all consistent partition relations on the real line with countably infinite exponents, and a characterisation of the statement "no uncountable-exponent partition relations hold on the real line", working throughout in ZF without the Axiom of Choice.

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Lyra A. Gardiner. 2025-07-16. Infinite-Exponent Partition Relations on the Real Line. https://arxiv.org/abs/2507.12361

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