{"paper":{"title":"Infinite monochromatic sumsets for colourings of the reals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.LO","authors_text":"D\\'aniel T. Soukup, Imre Leader, Paul A. Russell, P\\'eter Komj\\'ath, Saharon Shelah, Zolt\\'an Vidny\\'anszky","submitted_at":"2017-10-20T12:16:39Z","abstract_excerpt":"N. Hindman, I. Leader and D. Strauss proved that it is consistent that there is a finite colouring of $\\mathbb R$ so that no infinite sumset $X+X=\\{x+y:x,y\\in X\\}$ is monochromatic. Our aim in this paper is to prove a consistency result in the opposite direction: we show that, under certain set-theoretic assumptions, for any $c:\\mathbb R\\to r$ with $r$ finite there is an infinite $X\\subseteq \\mathbb R$ so that $c$ is constant on $X+X$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07500","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}