{"paper":{"title":"Finite big Ramsey degrees in universal structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dragan Masulovic","submitted_at":"2018-07-02T13:41:21Z","abstract_excerpt":"Big Ramsey degrees of finite structures are usually considered with respect to a Fra\\\"{i} ss\\'e limit. Building mainly on the work of Devlin, Sauer, Laflamme and Van Th\\'e, in this paper we consider structures which are not Fra\\\"{i} ss\\'e limits, and still have the property that their finite substructures have finite big Ramsey degrees in them. For example, the class of all finite acyclic oriented graphs is not a Fra\\\"{i} ss\\'e class, and yet we show that there is a countably infinite acyclic oriented graph in which every finite acyclic oriented graph has finite big Ramsey degree. Our main too"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00658","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"}