{"paper":{"title":"Characterization of NIP theories by ordered graph-indiscernibles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Lynn Scow","submitted_at":"2011-06-25T18:04:24Z","abstract_excerpt":"We generalize the Unstable Formula Theorem characterization of stable theories from \\citep{sh78}: that a theory $T$ is stable just in case any infinite indiscernible sequence in a model of $T$ is an indiscernible set. We use a generalized form of indiscernibles from \\citep{sh78}: in our notation, a sequence of parameters from an $L$-structure $M$, $(b_i : i \\in I)$, indexed by an $L'$-structure $I$ is \\emph{$L'$-generalized indiscernible in $M$} if qftp$^{L'}(\\ov{i};I)$=qftp$^{L'}(\\ov{j};I)$ implies tp$^L(\\ov{b}_{\\ov{i}}; M)$ = tp$^L(\\ov{b}_{\\ov{j}};M)$ for all same-length, finite $\\ov{i}, \\ov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5153","kind":"arxiv","version":2},"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"}