{"paper":{"title":"Tree property at successor of a singular limit of measurable cardinals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Mohammad Golshani","submitted_at":"2016-01-16T09:19:17Z","abstract_excerpt":"Assume $\\lambda$ is a singular limit of $\\eta$ supercompact cardinals, where $\\eta \\leq \\lambda$ is a limit ordinal. We present two forcing methods for making $\\lambda^+$ the successor of the limit of the first $\\eta$ measurable cardinals while the tree property holding at $\\lambda^+.$ The first method is then used to get, from the same assumptions, tree property at $\\aleph_{\\eta^2+1}$ with the failure of $SCH$ at $\\aleph_{\\eta^2}$. This extends results of Neeman and Sinapova. The second method is also used to get tree property at successor of an arbitrary singular cardinal, which extends some"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04139","kind":"arxiv","version":3},"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"}