Undecidability of indecomposable polynomial rings

IF 0.4 4区数学 Q4 LOGIC

Archive for Mathematical Logic Pub Date : 2024-08-12 DOI:10.1007/s00153-024-00936-3

Marco Barone, Nicolás Caro-Montoya, Eudes Naziazeno

引用次数: 0

Abstract

By using algebraic properties of (commutative unital) indecomposable polynomial rings we achieve results concerning their first-order theory, namely: interpretability of arithmetic and a uniform proof of undecidability of their full theory, both in the language of rings without parameters. This vastly extends the scope of a method due to Raphael Robinson, which deals with a restricted class of polynomial integral domains.

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不可分解多项式环的不可判定性

通过使用（交换单元）不可分解多项式环的代数性质，我们获得了有关其一阶理论的结果，即：算术的可解释性和其完整理论的不可判定性的统一证明，两者均使用无参数环语言。这极大地扩展了拉斐尔-罗宾逊（Raphael Robinson）提出的方法的范围，该方法处理的是一类受限制的多项式积分域。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Archive for Mathematical Logic 数学-数学

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期刊介绍： The journal publishes research papers and occasionally surveys or expositions on mathematical logic. Contributions are also welcomed from other related areas, such as theoretical computer science or philosophy, as long as the methods of mathematical logic play a significant role. The journal therefore addresses logicians and mathematicians, computer scientists, and philosophers who are interested in the applications of mathematical logic in their own field, as well as its interactions with other areas of research.