{"paper":{"title":"On definitions of polynomials over function fields of positive characteristi","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.NT","authors_text":"Alexandra Shlapentokh","submitted_at":"2015-02-09T22:28:56Z","abstract_excerpt":"We consider the problem of defining polynomials over function fields of positive characteristic. Among other results, we show that the following assertions are true.\n  1. Let $\\G_p$ be an algebraic extension of a field of $p$ elements and assume $\\G_p$ is not algebraically closed. Let $t$ be transcendental over $\\G_p$, and let $K$ be a finite extension of $\\G_p(t)$. In this case $\\G_p[t]$ has a definition (with parameters) over $K$ of the form $\\forall \\exists \\ldots \\exists P$ with only one variable in the range of the universal quantifier and $P$ being a polynomial over $K$.\n  2. For any $q$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02714","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"}