{"paper":{"title":"Corrigendum to the paper: Geometric Axioms for Differentially Closed Fields with Several Commuting Derivations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Omar Leon Sanchez","submitted_at":"2012-10-11T14:37:47Z","abstract_excerpt":"In the proof of Lemma 2.6 (2) the iteration of the map {\\tau} was not performed\nproperly and in fact the lemma is wrong; a counterexample is given by f = \\bar{x}_1and k = 2. This error does not, however, affect the geometric characterization given in Theorem 3.4 but only the attempt in Theorem 4.3 to express it as a first-order set of axioms. That attempt is incorrect; the main problem being that in general {\\tau}V(f_1,..., f_s) 6= V(f_1..., f_s, {\\tau}f_1,..., {\\tau}f_s). But a different, indeed simpler, set of first-order axioms, which we will now describe, does express the geometric charact"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3258","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"}