Conditions for Existence of Jonsson Hybrids

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2026-07-28 DOI:10.1007/s10469-026-09839-z

N. M. Mussina, I. O. Tungushbayeva, A. R. Yeshkeyev

引用次数: 0

Abstract

We investigate the existence of hybrids of Jonsson theories in various first-order languages. A general framework for hybrids is constructed, defined by ∀∃-sentences true in the Cartesian product of semantic models. For theories in the same language, examples of hybrids are provided; necessary and sufficient conditions for the existence of a hybrid in a functional signature are established; it is shown that a hybrid can inherit properties of the original theories (perfection, categoricity, stability). For theories in different languages, the existence of hybrids is proved for arbitrary enrichments of semantic models to the joint language, and an amalgam is constructed. It is shown that hybrids can differ depending on the enrichments.

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Jonsson杂化的存在条件

我们研究了Jonsson理论在各种一阶语言中混合的存在性。混合的一般框架被构造，定义为∀∃-句子在语义模型的笛卡尔积中为真。对于同一语言的理论，提供了混合的例子；建立功能签名中杂合存在的充分必要条件；结果表明，混合理论可以继承原理论的完备性、范畴性、稳定性等特性。对于不同语言的理论，证明了混合模型的存在性，可以任意地将语义模型充实到联合语言中，并构造了一个汞合金。结果表明，杂化体随富集程度的不同而不同。

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.