{"paper":{"title":"Model-theoretic dividing lines via posets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Dar\\'io Garc\\'ia, Rosario Mennuni","submitted_at":"2022-09-01T16:32:19Z","abstract_excerpt":"We show that for each property $\\mathsf{P}\\in \\{\\mathsf{OP}, \\mathsf{IP}, \\mathsf{TP}_1, \\mathsf{TP}_2, \\mathsf{ATP}, \\mathsf{SOP}_3\\}$ there is a poset $\\Sigma_{\\mathsf{P}}$ such that a theory has property $\\mathsf{P}$ if and only if some model interprets a poset in which $\\Sigma_{\\mathsf{P}}$ can be embedded. We also introduce a new property $\\mathsf{SUP}$, consistent with $\\mathsf{NIP}_2$ and implying $\\mathsf{ATP}$ and $\\mathsf{SOP}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.00571","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.00571/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}