{"paper":{"title":"Algebraically Closed Fields with a Generic Multiplicative Character","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Minh Chieu Tran, Tigran Hakobyan","submitted_at":"2017-04-30T01:38:52Z","abstract_excerpt":"We study the model theory of the $2$-sorted structure $(\\mathbb{F}, \\mathbb{C};\\chi)$, where $\\mathbb{F}$ is an algebraic closure of a finite field of characteristic $p$, $\\mathbb{C}$ is the field of complex numbers and $\\chi: \\mathbb{F} \\to \\mathbb{C}$ is an injective, multiplication preserving map. We obtain an axiomatization $\\mathrm{ACFC}_p$ of $\\mathrm{Th}(\\mathbb{F},\\mathbb{C};\\chi)$ in a suitable language $L$, classify the models of $\\mathrm{ACFC}_p$ up to isomorphism, prove a modified model companion result, give various descriptions of definable sets inside a model of $\\mathrm{ACFC}_p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00261","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"}