{"paper":{"title":"Fra\\\"iss\\'e limits of metric structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Ita\\\"i Ben Yaacov (ICJ)","submitted_at":"2012-03-20T15:05:49Z","abstract_excerpt":"We develop \\emph{Fra\\\"iss\\'e theory}, namely the theory of \\emph{Fra\\\"iss\\'e classes} and \\emph{Fra\\\"iss\\'e limits}, in the context of metric structures. We show that a class of finitely generated structures is Fra\\\"iss\\'e if and only if it is the age of a separable approximately homogeneous structure, and conversely, that this structure is necessarily the unique limit of the class, and is universal for it. We do this in a somewhat new approach, in which ''finite maps up to errors'' are coded by \\emph{approximate isometries}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4459","kind":"arxiv","version":4},"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"}