{"paper":{"title":"A global approach to AECs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Andr\\'es Villaveces, Hugo Luiz Mariano, Pedro Hernan Zambrano","submitted_at":"2014-05-18T10:49:51Z","abstract_excerpt":"In this work we present some general categorial ideas on Abstract Elementary Classes (AECs) %\\cite{She}, inspired by the totality of AECs of the form $(Mod(T), \\preceq)$, for a first-order theory T: (i) we define a natural notion of (funtorial) morphism between AECs; (ii) explore the following constructions of AECs: \"generalized\" theories, pullbacks of AECs, (Galois) types as AECs; (iii) apply categorial and topological ideas to encode model-theoretic notions on spaces of types %(see Michael Lieberman Phd thesis) ; (iv) present the \"local\" axiom for AECs here called \"local Robinson's property\""},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4488","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"}