We discuss the possibility of applying the compactness theorem to the study of finite structures. Given a class of finite structures, it is important to determine whether it can be expressed by a particular category of sentences. We are interested in this type of problem, and use nonstandard method for showing the non‐expressibility of certain classes of finite graphs by an existential monadic second order sentence.

中文翻译：

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有限结构的非标准方法

我们讨论了将紧性定理应用于有限结构研究的可能性。给定一类有限结构，确定它是否可以由特定类别的句子表示很重要。我们对这种类型的问题感兴趣，并使用非标准方法来显示存在的单子二阶句子对某些类有限图的不可表达性。