Infinite-Exponent Partition Relations on the Real Line
Logic
2026-04-08 v3 Combinatorics
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.
Keywords
Cite
@article{arxiv.2507.12361,
title = {Infinite-Exponent Partition Relations on the Real Line},
author = {Lyra A. Gardiner},
journal= {arXiv preprint arXiv:2507.12361},
year = {2026}
}
Comments
23 pages; replaced proof of Proposition 5 with one more suited to the setting of linear orders