High and Low Homogeneity

Siberian Advances in Mathematics Pub Date : 2021-04-03 DOI:10.1134/s1055134421010028

K. Zh. Kudaĭbergenov

引用次数: 0

Abstract

We find conditions such that every \(\lambda \)-homogeneous model with small \( \lambda \) satisfying these conditions is homogeneous. As a corollary, we obtain conditions guaranteeing that the following implication holds: If \(T \) is a theory, \(\mu >|T| \), and every model of \(T \) of cardinality \( \mu \) is \(\omega _1\) -homogeneous then every model of \(T\) of sufficiently large cardinality is homogeneous.

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高低同质性

摘要我们找到了所有具有小\( \lambda \)的\(\lambda \) -齐次模型都满足这些条件的条件。作为推论，我们得到了保证以下含义成立的条件:如果\(T \)是一个理论，\(\mu >|T| \)，并且每个\(T \)的基数\( \mu \)的模型都是\(\omega _1\) -齐次的，那么每个\(T\)的足够大基数的模型都是齐次的。

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

Siberian Advances in Mathematics Mathematics-Mathematics (all)

CiteScore

0.70

自引率

0.00%

发文量

期刊介绍： Siberian Advances in Mathematics is a journal that publishes articles on fundamental and applied mathematics. It covers a broad spectrum of subjects: algebra and logic, real and complex analysis, functional analysis, differential equations, mathematical physics, geometry and topology, probability and mathematical statistics, mathematical cybernetics, mathematical economics, mathematical problems of geophysics and tomography, numerical methods, and optimization theory.