{"paper":{"title":"On $\\mathbb R$-embeddability of almost disjoint families and Akemann-Doner C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.OA"],"primary_cat":"math.LO","authors_text":"Michael Hru\\v{s}\\'ak, Osvaldo Guzm\\'an, Piotr Koszmider","submitted_at":"2019-01-02T20:11:52Z","abstract_excerpt":"An almost disjoint family $\\mathcal A$ of subsets of $\\mathbb N$ is said to be $\\mathbb R$-embeddable if there is a function $f:\\mathbb N\\rightarrow \\mathbb R$ such that the sets $f[A]$ are ranges of real sequences converging to distinct reals for distinct $A\\in \\mathcal A$. It is well known that almost disjoint families which have few separations, such as Luzin families, are not $\\mathbb R$-embeddable. We study extraction principles related to $\\mathbb R$-embeddability and separation properties of almost disjoint families of $\\mathbb N$ as well as their limitations. An extraction principle wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.00517","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"}