Claims

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1965_03_01_erdos_hajnal_rado: Theorem I(iv) of Erdős, Hajnal and Rado (Acta Math. Acad. Sci. Hungar., 1965) gives the relation of Problem 1220 for every qualifying singular cardinal under GCH, so ZFC, if consistent, does not refute it.

1987_01_01_shelah_stanley: Shelah and Stanley (Ann. Pure Appl. Logic, 1987) force a counterexample to the relation of Problem 1220 at aleph_(c+), which meets both hypotheses in ZFC, so ZFC, if consistent, does not prove the universal statement.

2026_09_25_bae: Claims that ZFC, if consistent, does not prove the partition relation of Problem 1220 for every qualifying singular cardinal, through the Shelah-Stanley forcing of 1987, with the author's Lean 4 development.

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