{"paper":{"title":"Some Model Theoretic Properties of Non-AC Generic Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Ali N. Valizadeh, Massoud Pourmahdian","submitted_at":"2016-06-18T13:22:09Z","abstract_excerpt":"In the context of Hrushovski constructions we take a language $ \\mathcal{L} $ with a ternary relation $ R $ and consider the theory of the generic models $ M^{*}_{\\alpha}, $ of the class of finite $ \\mathcal{L}$-structures equipped with predimension functions $ \\delta_{\\alpha}, $ for $ \\alpha\\in(0,1]\\cap\\mathbb{Q} $. The theory of generic structures of non-AC smooth classes have been investigated from different points of view, including decidability and their power in interpreting known structures and theories. For a rational $ \\alpha\\in(0,1], $ first we prove that the theory of $ M^{*}_{\\alph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05750","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"}