Submission date: 4 April 2023

Abstract:

We provide a uniform interpretation of arithmetic in the class of polynomial rings in one variable over a field of positive characteristic. Afterwards we prove, more generally, 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.

Mathematics Subject Classification: 03B10, 03B25, 03C40, 13B25, 13F99, 16U99

Keywords and phrases:

Full text arXiv 2304.02165: pdf, ps.