The Theory of the Entire Algebraic Functions
Taylor Dupuy, Ehud Hrushovski · arXiv (Cornell University) · 2023
Let A be the integral closure of the ring of polynomials CC[t], within the field of algebraic functions in one variable. We show that A interprets the ring of integers. This contrasts with the analogue for finite fields, proved to have a decidable theory (see Prestel-Schmid and van den Dries-A. Macintyre).