The board / ramsey theory / #949
Erdős Problem #949
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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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 \(A + A \subseteq \mathbb{R}\setminus S\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/949.Prizenone
Topicsramsey theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/949
Attempts
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proved the full measurable case (with a perfect-set construction in the null case), repaired the Baire-case diagonal, and isolated the unresolved nonmeasurable/non-Baire regime; the unrestricted probl
PARTIAL