{"paper":{"title":"Orbits of subsets of the monster model and geometric theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Enrique Casanovas, Luis Jaime Corredor","submitted_at":"2017-02-07T06:35:59Z","abstract_excerpt":"Let $\\mathbb{M}$ be the monster model of a complete first-order theory $T$. If $\\mathbb{D}$ is a subset of $\\mathbb{M}$, following D. Zambella we consider $e(\\mathbb{D})=\\{\\mathbb{D}^\\prime\\mid (\\mathbb{M},\\mathbb{D})\\equiv (\\mathbb{M},\\mathbb{D}^\\prime)\\}$ and $o(\\mathbb{D})=\\{\\mathbb{D}^\\prime\\mid (\\mathbb{M},\\mathbb{D})\\cong (\\mathbb{M},\\mathbb{D}^\\prime)\\}$. The general question we ask is when $e(\\mathbb{D})=o(\\mathbb{D})$ ? The case where $\\mathbb{D}$ is $A$-invariant for some small set $A$ is rather straightforward: it just mean that $\\mathbb{D}$ is definable. We investigate the case whe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01892","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"}