Complete classification of all consistent countably infinite exponent partition relations on the reals together with a characterization of the statement that no uncountable-exponent relations hold, all proved in ZF.
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3 Pith papers cite this work. Polarity classification is still indexing.
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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.
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 the Real Line
Complete classification of all consistent countably infinite exponent partition relations on the reals together with a characterization of the statement that no uncountable-exponent relations hold, all proved in ZF.
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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.