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Erdős problem 199

If A⊂RA\subset \mathbb{R} does not contain a 3-term arithmetic progression then must R\A\mathbb{R}\backslash A contain an infinite arithmetic progression?

No current result

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

Retained declaration

FormalConjectures/ErdosProblems/199.lean

Formal Conjectures

FormalConjectures/ErdosProblems/199.leanErdos199.erdos_1991 lineExact file
False ↔ ∀ (A : Set ℝ), ThreeAPFree A → ∃ S, S.IsAPOfLength ⊤ ∧ S ⊆ Aᶜ
SolvedProof has a holelean4external proof

The proof uses `sorry`: part of the argument is written but not proved. Lean accepts the file; it does not accept the theorem.

Proof manifests naming this Problem

  • Jayyhk Erdős Leanjayyhk:erdos:199
  • PLBY Lean proofsErdosProblems.Erdos199

Reported activity

Work these sources record against this Problem. Source-reported attribution, not reviewed here.

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