The board / set theory / #592
Erdős Problem #592
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
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 \(K_3\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/592.Prize$1,000
Topicsset theory, ramsey theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/592
Attempts
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Reduced every unresolved positive instance to uniform three-way amalgamation of Schipperus game strategies, and proved that every endpoint-compatible alternating block pattern triangle-amalgamates (wi
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