{"paper":{"title":"Consequences of the existence of ample generics and automorphism groups of homogeneous metric structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Maciej Malicki","submitted_at":"2014-05-07T08:27:47Z","abstract_excerpt":"We define a simple criterion for a homogeneous, complete metric structure $X$ that implies that the automorphism group $\\mbox{Aut}(X)$ satisfies all the main consequences of the existence of ample generics: it has the small index property, the automatic continuity property, and uncountable cofinality for non-open subgroups. Then we verify it for the Urysohn space $\\mbox{U}$, the Lebesgue probability measure algebra $\\mbox{MALG}$, and the Hilbert space $\\ell_2$, thus proving that $\\mbox{Iso}(\\mbox{U})$, $\\mbox{Aut}(\\mbox{MALG})$, $U(\\ell_2)$, and $O(\\ell_2)$ share these properties. We also form"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1532","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"}