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.
Infinite-Exponent Partition Relations on the Real Line
2 Pith papers cite this work. Polarity classification is still indexing.
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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.
fields
math.LO 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Certain infinite-exponent partition relations on linear orders and graphs are consistent with ZF yet imply the negation of KWP₁ and the Ordering Principle.
citing papers explorer
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Infinite-Exponent Partition Relations on Higher Analogues of the Real Line
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.
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Structural Infinite-Exponent Partition Relations and Weak Choice Principles
Certain infinite-exponent partition relations on linear orders and graphs are consistent with ZF yet imply the negation of KWP₁ and the Ordering Principle.