Model Theory of Enriched Boolean Algebras

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2026-09-02 DOI:10.1007/s10469-026-09846-0

D. E. Pal’chunov, A. V. Trofimov

引用次数: 0

Abstract

We study enriched Boolean algebras. We describe subalgebras of Boolean algebras determined by fixed elements of automorphisms. We construct a continuum of superatomic Boolean algebras with a distinguished subalgebra whose elementary theories have no prime model. We investigate semigroups of elementary types of Boolean algebras with a distinguished subalgebra and of Boolean algebras with distinguished ideals.

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富布尔代数的模型理论

我们学习富布尔代数。我们描述了由自同构的固定元素决定的布尔代数的子代数。构造了一个具有特殊子代数的超原子布尔代数连续体，其初等理论没有素数模型。研究了具有显著子代数的布尔代数的初等型和具有显著理想的布尔代数的半群。

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

Algebra and Logic 数学-数学

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： This bimonthly journal publishes results of the latest research in the areas of modern general algebra and of logic considered primarily from an algebraic viewpoint. The algebraic papers, constituting the major part of the contents, are concerned with studies in such fields as ordered, almost torsion-free, nilpotent, and metabelian groups; isomorphism rings; Lie algebras; Frattini subgroups; and clusters of algebras. In the area of logic, the periodical covers such topics as hierarchical sets, logical automata, and recursive functions. Algebra and Logic is a translation of ALGEBRA I LOGIKA, a publication of the Siberian Fund for Algebra and Logic and the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences. All articles are peer-reviewed.