{"paper":{"title":"Ramsey theory for monochromatically well-connected subsets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Jeffrey Bergfalk","submitted_at":"2019-02-28T06:09:17Z","abstract_excerpt":"We define well-connectedness, an order-theoretic notion of largeness whose associated partition relations $\\nu\\to_{wc}(\\mu)_\\lambda^2$ formally weaken those of the classical Ramsey relations $\\nu\\to(\\mu)_\\lambda^2$. We show that it is consistent that the arrows $\\to_{wc}$ and $\\to$ are, in infinite contexts, essentially indistinguishable. We then show, in contrast, that in Mitchell's model of the tree property at $\\omega_2$, the relation $\\omega_2\\to_{wc}(\\omega_2)_\\omega^2$ does hold, and that the consistency strength of this relation holding is precisely a weakly compact cardinal. These inve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10912","kind":"arxiv","version":1},"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"}