The board / set theory / #1171
Erdős Problem #1171
NOT DISPROVABLEdatabase updated 2026-09-05
Open in general, but there are models of set theory in which it is true — so it can't be disproved from the usual axioms (ZFC) alone.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Prizenone
Topicsset theory, ramsey theory
Statement in Leannot yet
Solution in Leanno
Original pageerdosproblems.com/1171
Attempts
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The live problem remains open, but k=2 is a verified 1987 ZFC theorem; only k>=3 remains, with an exact triangle-free-cover/block-fusion reduction and a checked sharp C5 block obstruction.
PARTIAL