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.

中文翻译：

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高同质性和低同质性

摘要

我们发现条件使得每个\（\拉姆达\） -homogeneous小模型\（\拉姆达\）满足这些条件是均匀的。作为推论，我们获得低保下列蕴涵保持条件：如果\（T \）是一种理论，\（\亩> | T | \） ，和每一个模型\（T \）基数的\（\亩\）是\（\ omega _1 \）- 同质的，因此具有足够大基数的\（T \）的每个模型都是同质的。