不可分解多项式环的不可判定性

Pub Date : 2024-08-12 DOI:10.1007/s00153-024-00936-3

Marco Barone, Nicolás Caro-Montoya, Eudes Naziazeno

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引用次数: 0

摘要

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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Undecidability of indecomposable polynomial rings

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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