Erdős Problem 591

References:

• erdosproblems.com/591
• [Sc10] Schipperus, Rene, Countable partition ordinals. Ann. Pure Appl. Logic (2010), 1195-1215.

theorem Erdos591.erdos_591 : True ↔ OrdinalCardinalRamsey (Ordinal.omega0 ^ Ordinal.omega0 ^ 2) (Ordinal.omega0 ^ Ordinal.omega0 ^ 2) 3

Let $α$ be the infinite ordinal $\omega^{\omega^2}$. Is it true that any red/blue colouring of the edges of $K_α$ there is either a red $K_α$ or a blue $K_3$?

This is true and was proved independently by Schipperus [Sc10] and Darby.