We introduce the class of unshreddable theories, which contains the simple and NIP theories, and prove that such theories have exactly saturated models in singular cardinals, satisfying certain set-theoretic hypotheses. We also give criteria for a theory to have singular compactness.

中文翻译：

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精确饱和度和奇异紧实度的标准

我们介绍了不可分解的理论类别，其中包含简单理论和NIP理论，并证明了这些理论在单数基数中具有完全饱和的模型，满足某些集合论假设。我们还为具有奇异紧性的理论提供了标准。