The board / set theory / #1177
Erdős Problem #1177
OPENdatabase updated 2026-01-23
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).
Let \(G\) be a finite \(3\)-uniform hypergraph, and let \(F_G(\kappa)\) denote the collection of \(3\)-uniform hypergraphs with chromatic number \(\kappa\) not containing \(G\). If \(F_G(\aleph_1)\) is not empty then there exists \(X\in F_G(\aleph_1)\) of cardinality at most \(2^{2^{\aleph_0}}\). If both \(F_G(\aleph_1)\) and \(F_H(\aleph_1)\) are non-empty then \(F_G(\aleph_1)\cap F_H(\aleph_1)\) is non-empty. If \(\kappa,\lambda\) are uncountable cardinals and \(F_G(\kappa)\) is non-empty then \(F_G(\lambda)\) is non-empty.
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/1177.Prizenone
Topicsset theory, chromatic number, hypergraphs
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/1177
Attempts
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