{"paper":{"title":"A dependent theory with few indiscernibles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Itay Kaplan, Saharon Shelah","submitted_at":"2010-10-03T10:11:18Z","abstract_excerpt":"We give a full solution to the question of existence of indiscernibles in dependent theories by proving the following theorem: for every $\\theta$ there is a dependent theory $T$ of size $\\theta$ such that for all $\\kappa$ and $\\delta$, $\\kappa\\to\\left(\\delta\\right)_{T,1}$ iff $\\kappa\\to\\left(\\delta\\right)_{\\theta}^{<\\omega}$. This means that unless there are good set theoretical reasons, there are large sets with no indiscernible sequences."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0388","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"}