Elimination of quantifiers for a theory of real closed rings

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2024-07-06 DOI:10.1016/j.apal.2024.103494

Jorge I. Guier

引用次数: 0

Abstract

Let $T^{⁎}$ be the theory of lattice-ordered, convex subrings of von Neumann regular real closed rings that are divisible-projectable, sc-regular ([12]) and have no minimal (non zero) idempotents. In this paper, we introduce and study a local divisibility binary relation that, added to the language for lattice-ordered rings, together with the (usual) divisibility relation and the radical relation associated to the minimal prime spectrum ([19]) yields quantifier elimination for $T^{⁎}$ .

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实闭环理论的量词消除

让 T⁎ 成为冯-诺依曼正则实闭环的格有序凸子环理论，这些子环是可分投影的、sc 正则的（[12]），并且没有最小（非零）幂等子。在本文中，我们引入并研究了一种局部可分性二元关系，这种关系与（通常的）可分关系以及与最小素谱相关的基元关系（[19]）一起加入到格有序环的语言中，产生了 T⁎ 的量词消元。

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

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.