Elementary equivalence of rational function fields (Model Theory of Fields and its Applications)
Kenji Fukuzaki · Institutional Repositories DataBase (IRDB) · 2012
Let $K|k$ be a function field over a field $k$ .We suppose that $k$ is an algebraically closed field or a finite extension of a prime field.We prove that $K\equiv k(x)$ implies $K\cong k(t)$ , where $t$ is an indeterminate.For the case that $k$ is algebraically closed, this was proven by Duret (1992), and for the case that $k$ is a finite extension of a prime field, by Scanlon (2008).However we give a simple unified proof for both cases.