{"paper":{"title":"On model theory of covers of algebraically closed fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Kaisa Kangas, Tapani Hyttinen","submitted_at":"2015-02-03T21:34:50Z","abstract_excerpt":"We study covers of the multiplicative group of an algebraically closed field as quasiminimal pregeometry structures and prove that they satisfy the axioms for Zariski-like structures presented in \\cite{lisuriart}, section 4. These axioms are intended to generalize the concept of a Zariski geometry into a non-elementary context. In the axiomatization, it is required that for a structure $\\M$, there is, for each $n$, a collection of subsets of $\\M^n$, that we call the \\emph{irreducible sets}, satisfying certain properties. These conditions are generalizations of some qualities of irreducible clo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01042","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"}