{"paper":{"title":"Relatively exchangeable structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.LO","authors_text":"Harry Crane, Henry Towsner","submitted_at":"2015-09-22T19:10:15Z","abstract_excerpt":"We study random relational structures that are \\emph{relatively exchangeable}---that is, whose distributions are invariant under the automorphisms of a reference structure $\\mathfrak{M}$. When $\\mathfrak{M}$ has {\\em trivial definable closure}, every relatively exchangeable structure satisfies a general Aldous--Hoover-type representation. If $\\mathfrak{M}$ satisfies the stronger properties of {\\em ultrahomogeneity} and {\\em $n$-disjoint amalgamation property} ($n$-DAP) for every $n\\geq1$, then relatively exchangeable structures have a more precise description whereby each component depends loc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06733","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"}