The Number of Countable Models of a Complete Theory and of Its Inessential Extension

IF 0.6 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2025-09-05 DOI:10.1007/s10469-025-09789-y

K. Zh. Kudaibergenov

引用次数: 0

Abstract

It is proved that (a) there exists a complete countable theory having 2^ω countable models, some inessential extension of which has ω countable models, and that (b) there exists a complete countable theory having 2^ω countable models, some inessential extension of which has finitely many countable models. This gives an answer to the question of A. D. Taimanov.

查看原文本刊更多论文

完备理论的可数模型数及其非本质推广

证明了(a)存在一个具有2ω可数模型的完备可数理论，其非本质推广具有ω可数模型；(b)存在一个具有2ω可数模型的完备可数理论，其非本质推广具有有限多个可数模型。这就回答了a.d.泰马诺夫的问题。

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

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.