2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155636We prove that the first-order theory of any function field K of characteristic p>2 is undecidable in the language of rings without parameters. When K is a function field in one variable whose constant field is algebraic over a finite field, we can also prove undecidability in characteristic 2. The proof uses a result by Moret-Bailly about ranks of elliptic curves over function fields.12 pages; strengthened main theorem, proved undecidability in the language of rings without parametersNumber TheoryLogic11U05 (Primary); 03B25 (Secondary)text