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Erdős problem 949

Let S⊆RS \subseteq \mathbb{R} be a set containing no solutions to a+b=ca + b = c. Must there be a set A⊆R∖SA \subseteq \mathbb{R} \setminus S of cardinality continuum such that A+A⊆R∖SA + A \subseteq \mathbb{R}\setminus S?

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FormalConjectures/ErdosProblems/

949.lean

Retained formal statement1 of 2

Let S⊆RS \subseteq \mathbb{R} be a set containing no solutions to a+b=ca + b = c. Must there be a set A⊆R∖SA \subseteq \mathbb{R} \setminus S of cardinality continuum such that A+A⊆R∖SA + A \subseteq \mathbb{R}\setminus S?

FormalConjectures/ErdosProblems/949.leanErdos949.erdos_9491 lineExact file
True ↔ ∀ (S : Set ℝ), (∀ a ∈ S, ∀ b ∈ S, a + b ∉ S) → ∃ A ⊆ Sᶜ, Cardinal.mk ↑A = Cardinal.continuum ∧ A + A ⊆ Sᶜ
OpenStatement only, no proof

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