{"paper":{"title":"There may be no minimal non $\\sigma$-scattered linear orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Hossein Lamei Ramandi, Justin Tatch Moore","submitted_at":"2017-07-18T15:00:44Z","abstract_excerpt":"In this paper we demonstrate that it is consistent, relative to the existence of a supercompact cardinal, that there is no linear order which is minimal with respect to being non $\\sigma$-scattered. This shows that a theorem of Laver, which asserts that the class of $\\sigma$-scattered linear orders is well quasi-ordered, is sharp. We also prove that PFA${}^+$ implies that every non $\\sigma$-scattered linear order either contains a real type, an Aronszajn type, or a ladder system indexed by a stationary subset of $\\omega_1$, equipped with either the lexicographic or reverse lexicographic order."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05661","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"}