{"paper":{"title":"Distinguishing every finitely generated field of characteristic \\neq2 by a single field axiom","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Florian Pop","submitted_at":"2018-09-03T03:34:08Z","abstract_excerpt":"We show that the isomorphy type of every finitely generated field $K$ with $\\chr(K)\\neq2$ is encoded by a \\textit{\\textbf{single\\ha3explicit\\ha3axiom}} $\\istp K\\!$ \\textit{\\textbf{in\\ha3the\\ha3language\\ha3of\\ha3fields}}, i.e., for all finitely generated fields $L$ one has: $\\istp K$ holds in $L$ if and only if $K\\cong L$ as fields. This extends earlier results by \\nmnm{\\footnotesize\\sc Julia Robinson, Rumely, Poonen, Scanlon}, the author, and others."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00440","kind":"arxiv","version":3},"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"}