{"paper":{"title":"Pseudosaturation and the Interpretability Orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Douglas Ulrich","submitted_at":"2018-11-13T18:35:44Z","abstract_excerpt":"We streamline treatments of the interpretability orders $\\trianglelefteq^*_\\kappa$ of Shelah, the key new notion being that of pseudosaturation. Extending work of Malliaris and Shelah, we classify the interpretability orders on the stable theories. As a further application, we prove that for all countable theories $T_0, T_1$, if $T_1$ is unsupersimple, then $T_0 \\trianglelefteq^*_1 T_1$ if and only if $T_0 \\trianglelefteq^*_{\\aleph_1} T_1$. We thus deduce that simplicity is a dividing line in $\\trianglelefteq^*_{\\aleph_1}$, and that consistently, $SOP_2$ characterizes maximality in $\\trianglel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05448","kind":"arxiv","version":1},"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"}