FormalConjectures.ErdosProblems.«591»

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import FormalConjecturesUtil

Erdős Problem 591

References:

erdosproblems.com/591

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


open Cardinal Ordinal


namespace Erdos591


universe u

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.

@[category research solved, AMS 3]
theorem declaration uses 'sorry'erdos_591 : answer(True) ↔ OrdinalCardinalRamsey (ω ^ ω ^ 2) (ω ^ ω ^ 2) 3 := by⊢ True ↔ OrdinalCardinalRamsey (ω ^ ω ^ 2) (ω ^ ω ^ 2) 3
  sorryAll goals completed! 🐙


end Erdos591