{"paper":{"title":"On the mathematical and foundational significance of the uncountable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Dag Normann, Sam Sanders","submitted_at":"2017-11-24T12:21:50Z","abstract_excerpt":"We study the logical and computational properties of basic theorems of uncountable mathematics, including the Cousin and Lindel\\\"of lemma published in 1895 and 1903. Historically, these lemmas were among the first formulations of open-cover compactness and the Lindel\\\"of property, respectively. These notions are of great conceptual importance: the former is commonly viewed as a way of treating uncountable sets like e.g. $[0,1]$ as 'almost finite', while the latter allows one to treat uncountable sets like e.g. $\\mathbb{R}$ as 'almost countable'. This reduction of the uncountable to the finite/"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08939","kind":"arxiv","version":7},"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"}