{"paper":{"title":"Distributive Aronszajn trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Ari Meir Brodsky, Assaf Rinot","submitted_at":"2017-07-17T09:13:08Z","abstract_excerpt":"Ben-David and Shelah proved that if $\\lambda$ is a singular strong-limit cardinal and $2^\\lambda=\\lambda^+$, then $\\square^*_\\lambda$ entails the existence of a normal $\\lambda$-distributive $\\lambda^+$-Aronszajn tree. Here, it is proved that the same conclusion remains valid after replacing the hypothesis $\\square^*_\\lambda$ by $\\square(\\lambda^+,{<}\\lambda)$.\n  As $\\square(\\lambda^+,{<}\\lambda)$ does not impose a bound on the order-type of the witnessing clubs, our construction is necessarily different from that of Ben-David and Shelah, and instead uses walks on ordinals augmented with club "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05048","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"}