Virtual Algebraic Isomorphisms between Predicate Calculi of Finite Rich Signatures

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2022-05-03 DOI:10.1007/s10469-022-09666-y

M. G. Peretyat’kin

引用次数: 0

Abstract

It is proved that every two predicate calculi of finite rich signatures are algebraically virtually isomorphic, i.e., some of their Cartesian extensions are algebraically isomorphic. As an important application, it is stated that for predicate calculi in any two finite rich signatures, there exists a computable isomorphism between their Tarski–Lindenbaum algebras which preserves all model-theoretic properties of algebraic type corresponding to the real practice of research in model theory.

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有限富特征谓词演算之间的虚拟代数同构

证明了有限富签名的每两个谓词演算都是代数虚拟同构的，即它们的某些笛卡尔扩张是代数同构的。作为一个重要的应用，指出对于任意两个有限富签名中的谓词演算，它们的Tarski–Lindenbaum代数之间存在可计算同构，这保留了与模型理论研究的实际实践相对应的代数类型的所有模型论性质。

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.