{"paper":{"title":"Tree indiscernibilities, revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Byunghan Kim, Hyeung-Joon Kim, Lynn Scow","submitted_at":"2011-11-03T17:07:13Z","abstract_excerpt":"We give definitions that distinguish between two notions of indiscernibility for a set $\\{a_\\eta \\mid \\eta \\in \\W\\}$ that saw original use in \\cite{sh90}, which we name \\textit{$\\s$-} and \\textit{$\\n$-indiscernibility}. Using these definitions and detailed proofs, we prove $\\s$- and $\\n$-modeling theorems and give applications of these theorems. In particular, we verify a step in the argument that TP is equivalent to TP$_1$ or TP$_2$ that has not seen explication in the literature. In the Appendix, we exposit the proofs of \\citep[{App. 2.6, 2.7}]{sh90}, expanding on the details."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0915","kind":"arxiv","version":4},"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"}