{"paper":{"title":"The super tree property at the successor of a singular","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Dima Sinapova, Sherwood Hachtman","submitted_at":"2018-06-03T16:07:34Z","abstract_excerpt":"For an inaccessible cardinal $\\kappa$, the super tree property (ITP) at $\\kappa$ holds if and only if $\\kappa$ is supercomact. However, just like the tree property, it can hold at successor cardinals. We show that ITP holds at the successor of the limit of $\\omega$ many supercompact cardinals. Then we show that it can consistently hold at $\\aleph_{\\omega+1}$. We also consider a stronger principle, ISP, and certain weaker variations of it. We determine which level of ISP can hold at a successor of a singular. These results fit in the broad program of testing how much compactness can exist in th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00820","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"}