The board / set theory / #591
Erdős Problem #591
PROVEDdatabase updated 2026-01-17
The statement as posed is true, and a proof exists.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
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.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/591.Prize$250
Topicsset theory, ramsey theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/591
Attempts
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