Submission date: 30 January 2021

Abstract:

In [MacResField] the second author gave a systematic analysis of definability and decidability for rings M/pM, where M is a model of Peano Arithmetic and p is a prime in M.
In the present paper we extend those results to the more difficult case of M/p^kM, where M is a model of Peano Arithmetic, p is a prime in M, and k>1. In [MacResField] work of Ax on finite fields was used, here we use in addition work of Ax on ultraproduct of p-adics.

Mathematics Subject Classification: 03H15, 03C10

Keywords and phrases:

Full text arXiv 2102.00295: pdf, ps.