{"paper":{"title":"Model-theoretic applications of cofinality spectrum problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"M. Malliaris, S. Shelah","submitted_at":"2015-03-28T19:30:34Z","abstract_excerpt":"We apply the recently developed technology of cofinality spectrum problems to prove a range of theorems in model theory. First, we prove that any model of Peano arithmetic is $\\lambda$-saturated iff it has cofinality $\\geq \\lambda$ and the underlying order has no $(\\kappa, \\kappa)$-cuts for regular $\\kappa < \\lambda$. Second, assuming instances of GCH, we prove that $SOP_2$ characterizes maximality in the interpretability order $\\trianglelefteq^*$, settling a prior conjecture and proving that $SOP_2$ is a real dividing line. Third, we establish the beginnings of a structure theory for $NSOP_2$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08338","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":""},"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"}