{"paper":{"title":"Term inequalities in finite algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"David Hobby","submitted_at":"2016-01-19T13:16:18Z","abstract_excerpt":"Given an algebra $\\mathbf{A}$, and terms $s(x_{1},x_{2},\\dots x_{k})$ and $t(x_{1},x_{2},\\dots x_{k})$ of the language of ${\\mathbf A}$, we say that $s$ and $t$ are {\\em separated} in ${\\mathbf A}$ iff for all $a_{1},a_{2}\\dots a_{k}\\in A$, $s(a_{1},a_{2},\\dots a_{k})$ and $t(a_{1},a_{2},\\dots a_{k})$ are never equal. We prove that given two terms that are separated in any algebra, there exists a finite algebra in which they are separated. As a corollary, we obtain that whenever the sentence $\\sigma$ is a universally quantified conjunction of negated atomic formulas, $\\sigma$ is consistent iff"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04911","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"}