The model theory of residue rings of models of Peano Arithmetic: The prime power case

2021/01/30 by D'Aquino, P., Macintyre, A.
#03C10 #03H15 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2102.00295

Abstract

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

Related

• Finite and infinite primes in models of PA
• Expansions of the p-adic numbers that interprets the ring of integers
• Commutative unital rings elementarily equivalent to prescribed product rings
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• P-adic approximation of algebraic integers and residue class rings of rings of integer-valued polynomials