Erdős problem 949

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

Sources

The source's own material, retained exactly.

2 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

949.lean

Retained formal statement1 of 2

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

FormalConjectures/ErdosProblems/949.leanErdos949.erdos_9491 lineExact file

1True ↔ ∀ (S : Set ℝ), (∀ a ∈ S, ∀ b ∈ S, a + b ∉ S) → ∃ A ⊆ Sᶜ, Cardinal.mk ↑A = Cardinal.continuum ∧ A + A ⊆ Sᶜ

OpenStatement only, no proof