{"paper":{"title":"Model theory of fields with free operators in characteristic zero","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RA"],"primary_cat":"math.LO","authors_text":"Rahim Moosa, Thomas Scanlon","submitted_at":"2012-12-23T22:16:25Z","abstract_excerpt":"Generalising and unifying the known theorems for difference and differential fields, it is shown that for every finite free ${\\mathbb S}$-algebra ${\\mathcal D}$ over a field $A$ of characteristic zero the theory of ${\\mathcal D}$-fields has a model companion ${\\mathcal D}$-CF$_0$ which is simple and satisfies the Zilber dichotomy for finite-dimensional minimal types."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5838","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"}