{"paper":{"title":"The Halpern-L\\\"auchli Theorem at a Measurable Cardinal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Dan Hathaway, Natasha Dobrinen","submitted_at":"2016-08-01T20:01:05Z","abstract_excerpt":"Several variants of the Halpern-L\\\"auchli Theorem for trees of uncountable height are investigated. For $\\kappa$ weakly compact, we prove that the various statements are all equivalent. We show that the strong tree version holds for one tree on any infinite cardinal. For any finite $d \\ge 2$, we prove the consistency of the Halpern-L\\\"auchli Theorem on $d$ many $\\kappa$-trees at a measurable cardinal $\\kappa$, given the consistency of a $\\kappa+d$-strong cardinal. This follows from a more general consistency result at measurable $\\kappa$, which includes the possibility of infinitely many trees"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00592","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"}