Source labels openChecked July 26, 2026

Erdős Problem 564

Let $R_3(n)$ be the minimal $m$ such that if the edges of the $3$ -uniform hypergraph on $m$ vertices are $2$ -coloured then there is a monochromatic copy of the complete $3$ -uniform hypergraph on $n$ vertices.

Combinatorics AMS 5

Mathematical statement

Is there some constant $c>0$ such that $R_3(n) \geq 2^{2^{cn}}?$

Statement source: Erdős Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

erdos_564

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_564 : answer(sorry) ↔    ∃ c > 0, ∀ᶠ n in atTop, (2 : ℝ)^(2 : ℝ)^(c * n) ≤ hypergraphRamsey 3 n := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization erdosproblems.com/564background