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Erdős problem 965

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Erdős asks in [Er75b] if for every 2-coloring of ℝ, there is an uncountable set A⊆RA ⊆ ℝ such that all sums a+ba + b for a,b∈A,a≠ba, b ∈ A, a ≠ b have the same colour.

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2 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

965.lean

Retained formal statement2 of 2

In fact, in both [Ko16] and [SWCol] a generalized example for kk-sums is constructed.

FormalConjectures/ErdosProblems/965.leanErdos965.erdos_965.variants.generalization4 linesExact file
False ↔  ∀ k ≥ 2,    ∀ (f : ℝ → Fin 2),      ∃ A, ¬A.Countable ∧ ∀ (s t : Finset ℝ), ↑s ⊆ A → ↑t ⊆ A → s.card = k → t.card = k → f (s.sum id) = f (t.sum id)
SolvedStatement only, no proof