{"paper":{"title":"Two inequalities between cardinal invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Dilip Raghavan, Saharon Shelah","submitted_at":"2015-05-23T09:59:46Z","abstract_excerpt":"We prove two $\\mathrm{ZFC}$ inequalities between cardinal invariants. The first inequality involves cardinal invariants associated with an analytic P-ideal, in particular the ideal of subsets of $\\omega$ of asymptotic density $0$. We obtain an upper bound on the $\\ast$-covering number, sometimes also called the weak covering number, of this ideal by proving in Section \\ref{sec:covz0} that ${\\mathord{\\mathrm{cov}}}^{\\ast}({\\mathcal{Z}}_{0}) \\leq \\mathfrak{d}$. In Section \\ref{sec:skbk} we investigate the relationship between the bounding and splitting numbers at regular uncountable cardinals. W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06296","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"}