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Erdős problem 198

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The answer is no; Erdős and Graham report this was proved by Baumgartner, presumably referring to the paper [Ba75], which does not state this exactly, but the following simple construction is implicit in [Ba75].

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4 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

198.lean

Retained formal statement1 of 4

The statement for which Baumgartner actually writes a proof.

FormalConjectures/ErdosProblems/198.leanErdos198.baumgartner_headline2 linesExact file
∀ (V : Type u_1) [inst : AddCommGroup V] [Module ℚ V],  ∃ X, (∀ (Y : Set V), Y.IsAPOfLength ⊤ → (X ∩ Y).Nonempty) ∧ ∀ (Y : Set V), Y.IsAPOfLength 3 → (X ∩ Y).ncard ≤ 2
SolvedStatement only, no proof