Submission date: 20 May 2023

Abstract:

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).

Mathematics Subject Classification: 03C40

Keywords and phrases:

Full text arXiv 2305.12226: pdf, ps.