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import FormalConjecturesUtilErdős Problem 592
open Cardinal Ordinal
namespace Erdos592
universe u
Determine which countable ordinals $β$ have the property that, if $α = \omega^β$, then in any red/blue colouring of the edges of $K_α$ there is either a red $K_α$ or a blue $K_3$.
@[category research open, AMS 3]
theorem erdos_592 (β : Ordinal.{u}) : β.card ≤ ℵ₀ →
OrdinalCardinalRamsey (ω ^ β) (ω ^ β) 3 ↔ (answer(sorry) : Ordinal.{u} → Prop) β := β:Ordinal.{u}⊢ β.card ≤ ℵ₀ → OrdinalCardinalRamsey (ω ^ β) (ω ^ β) 3 ↔ sorry β
All goals completed! 🐙
-- TODO(firsching): add condition by Galvin and Larson.
end Erdos592