The board / set theory / #1169
Erdős Problem #1169
NOT DISPROVABLEdatabase updated 2026-01-24
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).
Is it true that \(\omega_1^2 \not\to (\omega_1^2, 3)^2\)? A problem of Erdős and Hajnal. Hajnal [Ha71] proved this assuming the continuum hypothesis. The source's displayed relation has blue target \(3\); its introductory \(k\) does not occur in that relation. See also [erdosproblems.com/592](https://www.erdosproblems.com/592).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/1169.Prizenone
Topicsset theory, ramsey theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/1169
Attempts
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