{"paper":{"title":"Aronszajn trees, square principles, and stationary reflection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Chris Lambie-Hanson","submitted_at":"2016-05-18T09:20:20Z","abstract_excerpt":"We investigate questions involving Aronszajn trees, square principles, and stationary reflection. We first consider two strengthenings of $\\square(\\kappa)$ introduced by Brodsky and Rinot for the purpose of constructing $\\kappa$-Souslin trees. Answering a question of Rinot, we prove that the weaker of these strengthenings is compatible with stationary reflection at $\\kappa$ but the stronger is not. We then prove that, if $\\mu$ is a singular cardinal, $\\square_\\mu$ implies the existence of a special $\\mu^+$-tree with a $\\mathrm{cf}(\\mu)$-ascent path, thus answering a question of L\\\"ucke."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05489","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"}