Erdős problem 847

Let $A \subset \mathbb{N}$ be an infinite set for which there exists some $\epsilon > 0$ such that in any subset of $A$ of size $n$ there is a subset of size at least $\epsilon n$ which contains no three-term arithmetic progression.

No current result

No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

FormalConjectures/ErdosProblems/847.lean

Formal Conjectures

FormalConjectures/ErdosProblems/847.leanErdos847.erdos_8471 lineExact file

1False ↔ ∀ (A : Set ℕ), Infinite ↑A → Erdos847.HasFew3APs A → ∃ n S, (∀ (i : Fin n), ThreeAPFree (S i)) ∧ A = ⋃ i, S i

SolvedStatement only, no proof

Reported by these sources. Not reviewed here.