{"paper":{"title":"Minimal obstructions for normal spanning trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CO","authors_text":"Max Pitz, Nathan Bowler, Stefan Geschke","submitted_at":"2016-09-05T07:34:21Z","abstract_excerpt":"Diestel and Leader have characterised connected graphs that admit a normal spanning tree via two classes of forbidden minors. One class are Halin's $(\\aleph_0,\\aleph_1)$-graphs: bipartite graphs with bipartition $(\\mathbb{N},B)$ such that $B$ is uncountable and every vertex of $B$ has infinite degree.\n  Our main result is that under Martin's Axiom and the failure of the Continuum Hypothesis, the class of forbidden $(\\aleph_0,\\aleph_1)$-graphs in Diestel and Leader's result can be replaced by one single instance of such a graph.\n  Under CH, however, the class of $(\\aleph_0,\\aleph_1)$-graphs con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01042","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"}