{"paper":{"title":"Uncountable strongly surjective linear orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"D\\'aniel T. Soukup","submitted_at":"2017-06-30T12:17:26Z","abstract_excerpt":"A linear order $L$ is strongly surjective if $L$ can be mapped onto any of its suborders in an order preserving way. We prove various results on the existence and non-existence of uncountable strongly surjective linear orders answering questions of Camerlo, Carroy and Marcone. In particular, $\\diamondsuit^+$ implies the existence of a lexicographically ordered Suslin-tree which is strongly surjective and minimal; every strongly surjective linear order must be an Aronszajn type under $2^{\\aleph_0}<2^{\\aleph_1}$ or in the Cohen and other canonical models (where $2^{\\aleph_0}=2^{\\aleph_1}$); fina"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.10171","kind":"arxiv","version":2},"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"}