{"paper":{"title":"On cuts in ultraproducts of linear orders II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Mohammad Golshani, Saharon Shelah","submitted_at":"2016-04-20T18:00:57Z","abstract_excerpt":"We continue our study of the class $\\mathscr{C}(D)$, where $D$ is a uniform ultrafilter on a cardinal $\\kappa$ and $\\mathscr{C}(D)$ is the class of all pairs $(\\theta_1, \\theta_2),$ where $(\\theta_1, \\theta_2)$ is the cofinality of a cut in $J^\\kappa /D$ and $J$ is some $(\\theta_1+\\theta_2)^+$-saturated dense linear order. We give a combinatorial characterization of the class $\\mathscr{C}(D)$. We also show that if $(\\theta_1, \\theta_2) \\in \\mathscr{C}(D)$ and $D$ is $\\aleph_1$-complete or $\\theta_1 + \\theta_2 > 2^\\kappa,$ then $\\theta_1=\\theta_2.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06044","kind":"arxiv","version":3},"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"}