The board / set theory / #590
Erdős Problem #590
PROVED LEANdatabase updated 2026-08-23
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Let \(α\) be the infinite ordinal \(\omega^{\omega}\). It was proved by Chang [Ch72] that any red/blue colouring of the edges of \(K_α\) there is either a red \(K_α\) or a blue \(K_3\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 3 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/590.Prize$250
Topicsset theory, ramsey theory
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/590
Attempts
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