green_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 $n → ∞$?

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

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