{"paper":{"title":"Infinite dimensional sequential compactness: Sequential compactness based on barriers","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.CO","math.LO"],"primary_cat":"math.GN","authors_text":"Carlos Lopez-Callejas, Cesar Corral, Osvaldo Guzman, Paul Szeptycki, Pourya Memarpanahi, Stevo Todorcevic","submitted_at":"2023-09-08T15:52:42Z","abstract_excerpt":"We introduce a generalization of sequential compactness using barriers on $\\omega$ extending naturally the notion introduced in [W. Kubi\\'{s} and P. Szeptycki, On a topological Ramsey theorem, \\emph{Canad. Math. Bull.}, 66 (2023), {156}--{165}]. We improve results from [C. Corral and O. Guzm{\\'a}n and C. L{\\'o}pez-Callejas, High dimensional sequential compactness, \\emph{Fund. Math.}] by building spaces that are $\\mathcal{B}$-sequentially compact but no $\\mathcal{C}$-sequentially compact when the barriers $\\mathcal{B}$ and $\\mathcal{C}$ satisfy certain rank assumption which turns out to be equi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.04397","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.04397/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}