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arXiv · 2102.00295

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

P. D'Aquino·A. Macintyre
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Abstract

In \cite{MacResField} 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 \cite{MacResField} work of Ax on finite fields was used, here we use in addition work of Ax on ultraproduct of $p$-adics.

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BibTeXRIS

P. D'Aquino, A. Macintyre. 2021-01-30. The model theory of residue rings of models of Peano Arithmetic: The prime power case. https://arxiv.org/abs/2102.00295

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