{"paper":{"title":"The Tukey Order and Subsets of $\\omega_1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Ana Mamatelashvili, Paul Gartside","submitted_at":"2016-08-01T04:44:10Z","abstract_excerpt":"One partially ordered set, $Q$, is a Tukey quotient of another, $P$, if there is a map $\\phi : P \\to Q$ carrying cofinal sets of $P$ to cofinal sets of $Q$. Two partial orders which are mutual Tukey quotients are said to be Tukey equivalent. Let $X$ be a space and denote by $\\mathcal{K}(X)$ the set of compact subsets of $X$, ordered by inclusion. The principal object of this paper is to analyze the Tukey equivalence classes of $\\mathcal{K}(S)$ corresponding to various subspaces $S$ of $\\omega_1$, their Tukey invariants, and hence the Tukey relations between them. It is shown that $\\omega^\\omeg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00319","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"}