{"paper":{"title":"Properties of simple density ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Adam Kwela, Jacek Tryba, Jaros{\\l}aw Swaczyna, Micha{\\l} Pop{\\l}awski","submitted_at":"2017-11-06T23:33:00Z","abstract_excerpt":"Let $G$ consist of all functions $g \\colon \\omega \\to [0,\\infty)$ with $g(n) \\to \\infty$ and $\\frac{n}{g(n)} \\nrightarrow 0$. Then for each $g\\in G$ the family $\\mathcal{Z}_g=\\{A\\subseteq\\omega:\\ \\lim_{n\\to\\infty}\\frac{\\text{card}(A\\cap n)}{g(n)}=0\\}$ is an ideal associated to the notion of so-called upper density of weight $g$. Although those ideals have recently been extensively studied, they do not have their own name. In this paper, for Reader's convenience, we propose to call them simple density ideals.\n  We show that there are $\\mathfrak{c}$ many non-isomorphic (in fact even incomparable"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02663","kind":"arxiv","version":2},"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"}