Isomorphism of Atomless Boolean Algebras with Distinguished Ideals

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2025-04-29 DOI:10.1007/s10469-025-09781-6

S. S. Goncharov, J. Xiang

引用次数: 0

Abstract

An algebraic, model-theoretic, and algorithmic theory of enriched Boolean algebras with distinguished ideals was developed in a series of papers by D. E. Pal’chunov, A. Touraille, P. E. Alaev, N. T. Kogabaev, and other authors. Here we study the problem on the number of countable Boolean algebras with distinguished ideals for the case when an algebra and its quotient with respect to a distinguished ideal are atomless. It is proved that, for this subclass, there exist continuum many such countable structures.

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具有杰出理想的无原子布尔代数的同构

D. E. Pal 'chunov, a . Touraille， P. E. Alaev， N. T. Kogabaev和其他作者在一系列论文中发展了具有杰出理想的富布尔代数的代数、模型论和算法理论。本文研究了当一个代数及其商相对于一个可分辨理想是无原子的情况下，具有可分辨理想的可数布尔代数的个数问题。证明了对于这个子类，存在连续的许多这样的可数结构。

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.