{"paper":{"title":"Weak Distributivity Implying Distributivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Dan Hathaway","submitted_at":"2014-10-08T03:04:59Z","abstract_excerpt":"Let $\\mathbb{B}$ be a complete Boolean algebra. We show, as an application of a previous result of the author, that if $\\lambda$ is an infinite cardinal and $\\mathbb{B}$ is weakly $(\\lambda^\\omega, \\omega)$-distributive, then $\\mathbb{B}$ is $(\\lambda, 2)$-distributive. Using a parallel result, we show that if $\\kappa$ is a weakly compact cardinal such that $\\mathbb{B}$ is weakly $(2^\\kappa, \\kappa)$-distributive and $\\mathbb{B}$ is $(\\alpha, 2)$-distributive for each $\\alpha < \\kappa$, then $\\mathbb{B}$ is $(\\kappa, 2)$-distributive."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1970","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"}