{"paper":{"title":"Splitting chains, tunnels and twisted sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.GN"],"primary_cat":"math.LO","authors_text":"Antonio Avil\\'es, David Chodounsk\\'y, F\\'elix Cabello S\\'anchez, Osvaldo Guzm\\'an, Piotr Borodulin-Nadzieja","submitted_at":"2019-07-23T08:13:48Z","abstract_excerpt":"We study splitting chains in $\\mathscr{P}(\\omega)$, that is, families of subsets of $\\omega$ which are linearly ordered by $\\subseteq^*$ and which are splitting. We prove that their existence is independent of axioms of $\\mathsf{ZFC}$. We show that they can be used to construct certain peculiar Banach spaces: twisted sums of $C(\\omega^*)=\\ell_\\infty/c_0$ and $c_0(\\mathfrak c)$. Also, we consider splitting chains in a topological setting, where they give rise to the so called tunnels."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09743","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"}