{"paper":{"title":"Strong tree Properties for two successive cardinals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Laura Fontanella","submitted_at":"2011-10-31T10:02:58Z","abstract_excerpt":"An inaccessible cardinal $\\kappa$ is supercompact when $(\\kappa, \\lambda)$-ITP holds for all $\\lambda\\geq \\kappa.$ We prove that if there is a model of $\\ZFC$ with two supercompact cardinals, then there is a model of \\ZFC where simultaneously $(\\aleph_2, \\mu)$-ITP and $(\\aleph_3, \\mu')$-ITP hold, for all $\\mu\\geq \\aleph_2$ and $\\mu'\\geq \\aleph_3.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6736","kind":"arxiv","version":5},"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"}