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Source labels openChecked July 26, 2026

Erdős ProblemsCombinatorics

Erdős Problem 1167

r=2r = 2 case.* The stepping-down from 3-uniform to 2-uniform partition relations: 2λ→(κα+1)α<γ32^\lambda \to (\kappa_\alpha + 1)_{\alpha<\gamma}^3 implies λ→(κα)α<γ2\lambda \to (\kappa_\alpha)_{\alpha<\gamma}^2. Generalises the classical Erdős–Rado stepping-up/down theorem ...

CombinatoricsAMS 5

Mathematical statement

r=2r = 2 case.* The stepping-down from 3-uniform to 2-uniform partition relations: 2λ→(κα+1)α<γ32^\lambda \to (\kappa_\alpha + 1)_{\alpha<\gamma}^3 implies λ→(κα)α<γ2\lambda \to (\kappa_\alpha)_{\alpha<\gamma}^2. Generalises the classical Erdős–Rado stepping-up/down theorem for pairs.

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

r_eq_two

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem r_eq_two (lam : Cardinal.{u}) (hlam : ℵ₀ ≤ lam)    (γ : Ordinal.{u}) (hγ : 2 ≤ γ) (κ : γ.ToType → Cardinal.{u}) :    cardinalPartitionRel ((2 : Cardinal.{u}) ^ lam) 3 γ (fun α => κ α + 1) →    cardinalPartitionRel lam 2 γ κ := 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 sourceformalizationerdosproblems.com/1167background