Source labels openChecked July 26, 2026

Ben Green's Open Problem 1

Let $A$ be a set of $n$ positive integers. Does $A$ contain a sum-free set of size at least $\frac n 3 + Ω(n)$ , where $Ω(n) → ∞$ as $n → ∞$ ?

Combinatorics AMS 5 AMS 11

Mathematical statement

Let $A$ be a set of $n$ positive integers. Does $A$ contain a sum-free set of size at least $\frac n 3 + Ω(n)$ , where $Ω(n) → ∞$ as $n → ∞$ ?

Statement source: Green's Open 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

green_1

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem green_1 : answer(sorry) ↔ ∃ Ω : ℕ → ℝ, atTop.Tendsto Ω atTop ∧     ∀ n, ∀ (A : Finset ℕ), (∀ a ∈ A, 0 < a) → A.card = n →     ∃ (S : Finset ℕ), S ⊆ A ∧ IsSumFree (S : Set ℕ) ∧ ((n : ℝ) / 3) + Ω n ≤ S.card := 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 Ben Green's Open Problem 1background