{"paper":{"title":"On the arithmetic of density","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Menachem Kojman","submitted_at":"2015-10-08T18:08:07Z","abstract_excerpt":"The $\\kappa$-density of a cardinal $\\mu\\ge\\kappa$ is the least cardinality of a dense collection of $\\kappa$-subsets of $\\mu$ and is denoted by $\\mathcal D(\\mu,\\kappa)$. The Singular Density Hypothesis (SDH) for a singular cardinal $\\mu$ of cofinality $cf\\mu=\\kappa$ is the equation $\\mathcal D(\\mu,\\kappa)=\\mu^+$. The Generalized Density Hypothesis (GDH) for $\\mu$ and $\\lambda$ such that $\\lambda\\le\\mu$ is: $\\mathcal D(\\mu,\\lambda)=\\mu$ if $cf\\mu\\not=cf\\lambda$ and $\\mathcal D(\\mu,\\lambda)=\\mu^+$ if $cf\\mu=cf\\lambda$.\n  Density is shown to satisfy Silver's theorem. The most important case is:\n "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02429","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"}