{"paper":{"title":"Borel's Conjecture in Topological Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.GR"],"primary_cat":"math.LO","authors_text":"Fred Galvin, Marion Scheepers","submitted_at":"2011-07-27T05:05:29Z","abstract_excerpt":"We introduce a natural generalization of Borel's Conjecture. For each infinite cardinal number $\\kappa$, let {\\sf BC}$_{\\kappa}$ denote this generalization. Then ${\\sf BC}_{\\aleph_0}$ is equivalent to the classical Borel conjecture. Assuming the classical Borel conjecture, $\\neg{\\sf BC}_{\\aleph_1}$ is equivalent to the existence of a Kurepa tree of height $\\aleph_1$. Using the connection of ${\\sf BC}_{\\kappa}$ with a generalization of Kurepa's Hypothesis, we obtain the following consistency results:\n  (1)If it is consistent that there is a 1-inaccessible cardinal then it is consistent that ${\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5383","kind":"arxiv","version":2},"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"}