{"paper":{"title":"Towers and gaps at uncountable cardinals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"D\\'aniel T. Soukup, Diana Carolina Montoya, Jonathan Schilhan, Vera Fischer","submitted_at":"2019-06-03T14:41:26Z","abstract_excerpt":"Our goal is to study the pseudo-intersection and tower numbers on uncountable regular cardinals, whether these two cardinal characteristics are necessarily equal, and related problems on the existence of gaps. First, we prove that either $\\mathfrak p(\\kappa)=\\mathfrak t(\\kappa)$ or there is a $(\\mathfrak p(\\kappa),\\lambda)$-gap of club-supported slaloms for some $\\lambda< \\mathfrak p(\\kappa)$. While the existence of such gaps is unclear, this is a promising step to lift Malliaris and Shelah's proof of $\\mathfrak p=\\mathfrak t$ to uncountable cardinals. We do analyze gaps of slaloms and, in par"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.00843","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"}