Constructive quantifier elimination with a focus on matrix rings

IF 0.8 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2026-05-01 Epub Date: 2025-12-22 DOI:10.1016/j.apal.2025.103706

Max Illmer, Tim Netzer

引用次数: 0

Abstract

We give a sufficient condition for a model theoretic structure B to ‘inherit’ quantifier elimination from another structure A. This yields an alternative proof of one of the main results from [8], namely quantifier elimination for certain matrix rings. The original proof uses model theory, and while it is very elegant and insightful, the proof we propose is much shorter and provides a constructive algorithm.

查看原文本刊更多论文

以矩阵环为重点的建设性量词消去

我们给出了模型理论结构B从另一个结构a“继承”量词消去的一个充分条件。这产生了[8]的一个主要结果的替代证明，即某些矩阵环的量词消去。最初的证明使用了模型理论，虽然它非常优雅和富有洞察力，但我们提出的证明要短得多，并提供了一个建设性的算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.