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.
Schilhan, Structural infinite-exponent partition relations and weak choice principles, in preparation
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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.