{"paper":{"title":"Suslin trees, the bounding number, and partition relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Dilip Raghavan, Stevo Todorcevic","submitted_at":"2016-02-25T12:22:37Z","abstract_excerpt":"We investigate the unbalanced ordinary partition relations of the form $\\lambda \\rightarrow {(\\lambda, \\alpha)}^{2}$ for various values of the cardinal $\\lambda$ and the ordinal $\\alpha$. For example, we show that for every infinite cardinal $\\kappa,$ the existence of a ${\\kappa}^{+}-$Suslin tree implies ${\\kappa}^{+} \\not\\rightarrow {\\left( {\\kappa}^{+}, {\\log}_{\\kappa}({\\kappa}^{+}) + 2 \\right)}^{2}$. The consistency of the positive partition relation $\\mathfrak{b} \\rightarrow {(\\mathfrak{b}, \\alpha)}^{2}$ for all $\\alpha < {\\omega}_{1}$ for the bounding number $\\mathfrak{b}$ is also establi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07901","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"}