We initiate a systematic investigation of the abstract elementary classes that have amalgamation, satisfy tameness (a locality property for orbital types), and are stable (in terms of the number of orbital types) in some cardinal. Assuming the singular cardinal hypothesis (SCH), we prove a full characterization of the (high-enough) stability cardinals, and connect the stability spectrum with the behavior of saturated models.We deduce (in ZFC) that if a class is stable on a tail of cardinals, then it has no long splitting chains (the converse is known). This indicates that there is a clear notion of superstability in this framework.We also present an application to homogeneous model theory: for [Formula: see text] a homogeneous diagram in a first-order theory [Formula: see text], if [Formula: see text] is both stable in [Formula: see text] and categorical in [Formula: see text] then [Formula: see text] is stable in all [Formula: see text].

中文翻译：

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趋向于驯服抽象基本类的稳定性理论

我们对具有融合性、满足驯服性（轨道类型的局部属性）以及在某些基数中稳定（就轨道类型的数量而言）的抽象基本类进行了系统研究。假设奇异基数假设（SCH），我们证明了（足够高的）稳定性基数的完整表征，并将稳定性谱与饱和模型的行为联系起来。我们推断（在 ZFC 中）如果一个类在红衣主教的尾巴，那么它没有长的分裂链（反过来是已知的）。这表明在这个框架中有一个明确的超稳定性概念。我们还提出了一个齐次模型理论的应用：对于[公式：见文本]一阶理论[公式：见文本]中的齐次图，如果 [公式：见文本] ：见文字]在[公式：