{"paper":{"title":"On universal modules with pure embeddings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.RA"],"primary_cat":"math.LO","authors_text":"Marcos Mazari-Armida, Thomas G. Kucera","submitted_at":"2019-03-01T17:12:09Z","abstract_excerpt":"We show that certain classes of modules have universal models with respect to pure embeddings.\n  $Theorem.$ Let $R$ be a ring, $T$ a first-order theory with an infinite model extending the theory of $R$-modules and $K^T=(Mod(T), \\leq_{pp})$ (where $\\leq_{pp}$ stands for pure submodule). Assume $K^T$ has joint embedding and amalgamation.\n  If $\\lambda^{|T|}=\\lambda$ or $\\forall \\mu < \\lambda( \\mu^{|T|} < \\lambda)$, then $K^T$ has a universal model of cardinality $\\lambda$.\n  As a special case we get a recent result of Shelah [Sh17, 1.2] concerning the existence of universal reduced torsion-free"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00414","kind":"arxiv","version":5},"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/1903.00414/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"}