{"paper":{"title":"Some model theory of fibrations and algebraic reductions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.LO","authors_text":"Anand Pillay, Rahim Moosa","submitted_at":"2012-10-10T02:48:06Z","abstract_excerpt":"Let p=tp(a/A) be a stationary type in an arbitrary finite rank stable theory, and P an A-invariant family of partial types. The following property is introduced and characterised: whenever c is definable over (A,a) and a is not algebraic over (A,c) then \\tp(c/A) is almost internal to P. The characterisation involves among other things an apparently new notion of ``descent\" for stationary types. Motivation comes partly from results in Section~2 of [Campana, Oguiso, and Peternell. Non-algebraic hyperk\\\"ahler manifolds. Journal of Differential Geometry, 85(3):397--424, 2010] where structural prop"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2793","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"}