Remarks on undecidability of indecomposable polynomial rings

Abstract

We prove that arithmetic is interpretable in any indecomposable polynomial ring (in any set of variables), and in addition we provide an alternative uniform proof of undecidability for all members in this class of rings.

In this new version we added another result about the interpretation of arithmetic for univariate polynomial rings over fields containing elements that are not roots of unity, and corrected some typos as well