{"paper":{"title":"A negative result on algebraic specifications of the meadow of rational numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.RA","authors_text":"Inge Bethke, Jan A. Bergstra","submitted_at":"2015-07-02T12:38:46Z","abstract_excerpt":"$\\mathbb{Q}_0$ - the involutive meadow of the rational numbers - is the field of the rational numbers where the multiplicative inverse operation is made total by imposing $0^{-1}=0$. In this note, we prove that $\\mathbb{Q}_0$ cannot be specified by the usual axioms for meadows augmented by a finite set of axioms of the form $(1+ \\cdots +1+x^2)\\cdot (1+ \\cdots +1 +x^2)^{-1}=1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00548","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"}