pith. machine review for the scientific record. sign in

arxiv: 2507.12361 · v3 · submitted 2025-07-16 · 🧮 math.LO · math.CO

Recognition: unknown

Infinite-Exponent Partition Relations on the Real Line

Lyra A. Gardiner
Authors on Pith no claims yet
classification 🧮 math.LO math.CO
keywords linepartitionrealrelationsinfinite-exponentarbitraryaxiomcharacterisation
0
0 comments X
read the original 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.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Infinite-Exponent Partition Relations on Higher Analogues of the Real Line

    math.LO 2026-05 unverdicted novelty 6.0

    A full classification of ⟨^α2, <lex⟩ → (τ)^τ is obtained for countable τ in ZF, via new results on infinite-exponent partition relations on higher real-line analogues.