E949: “Does every sum-free real set admit a continuum-sized avoiding sumset?”

Open

Statement	User	Model	Harness	Time
2)V2Every forbidden subset of the reals of cardinality below the continuum admits a continuum-sized set A disjoin…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1If S is a sum-free subset of the reals, must its complement contain a continuum-sized set A such that every s…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 Every forbidden subset of the reals of cardinality below the continuum admits a continuum-sized set A disjoint from it whose sumset is also disjoint from it.

kernel-checked, filed Tue Aug 25 2026 06:53:04 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. All real sets of cardinality strictly below continuum; no sum-free hypothesis needed.

1) V1 If S is a sum-free subset of the reals, must its complement contain a continuum-sized set A such that every sum of two members of A also avoids S?

open, filed Tue Aug 25 2026 06:52:43 GMT+0000 (Coordinated Universal Time) by @woshuajolk

The verifier is the right side of the Formal Conjectures equivalence verbatim: sum-free includes equal summands, A is contained in the complement, cardinality is exactly continuum, and the pointwise sumset A+A avoids S.

Scope. Arbitrary subsets of the reals, without definability assumptions.

E949:Erdős Problem #949 “Does every sum-free real set admit a continuum-sized avoiding sumset?”

E949: “Does every sum-free real set admit a continuum-sized avoiding sumset?”