AEC中的饱和模型链
Chains of saturated models in AECs
摘要：
我们研究了当一个饱和模型的联合是饱和的驯服抽象基本类（AEC）与合并的框架。我们证明：$\mathbf{Theorem}$如果$K$是一个驯服的AEC，其合并满足超稳定性的自然定义（这是从足够高的基数中的范畴性得出的），那么对于所有足够高的$λ$：* $λ$-饱和模型的递增链的并集是$λ$-饱和的。* 存在一个类型完全的好$λ$框架，其底层类是大小为$λ$的饱和模型。* 存在唯一的大小为$λ$的极限模型。我们的证明使用独立演算和推广的平均值，这个非一阶上下文。
英文摘要：
We study when a union of saturated models is saturated in the framework of tame abstract elementary classes (AECs) with amalgamation. We prove: $\mathbf{Theorem}$ If $K$ is a tame AEC with amalgamation satisfying a natural definition of superstability (which follows from categoricity in a high-enough cardinal), then for all high-enough $λ$: * The union of an increasing chain of $λ$-saturated models is $λ$-saturated. * There exists a type-full good $λ$-frame with underlying class the saturated models of size $λ$. * There exists a unique limit model of size $λ$. Our proofs use independence calculus and a generalization of averages to this non first-order context.
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