从两个连续的良好帧驯服
Tameness from two successive good frames
摘要：
我们表明，假设一个温和的集合论假设，如果一个抽象的基本类（AEC）有一个超稳定的分叉概念的模型的基数$λ$和一个超稳定的分叉概念的模型的基数$λ^+$，然后轨道类型的模型的基数$λ^+$由它们的限制子模型的基数$λ$。这里所说的超稳定分叉概念，是指一个好的框架，这是Shelah关于AEC的书中的一个中心概念。众所周知，轨道型的局部性与基数模型$λ$的超稳定概念的存在一起暗示基数模型$λ^+$的超稳定概念的存在，但在这里我们证明了相反的情况。一个直接的结果是$λ^+$中的分叉可以用$λ$中的分叉来描述。
英文摘要：
We show, assuming a mild set-theoretic hypothesis, that if an abstract elementary class (AEC) has a superstable-like forking notion for models of cardinality $λ$ and a superstable-like forking notion for models of cardinality $λ^+$, then orbital types over models of cardinality $λ^+$ are determined by their restrictions to submodels of cardinality $λ$. By a superstable-like forking notion, we mean here a good frame, a central concept of Shelah's book on AECs. It is known that locality of orbital types together with the existence of a superstable-like notion for models of cardinality $λ$ implies the existence of a superstable-like notion for models of cardinality $λ^+$, but here we prove the converse. An immediate consequence is that forking in $λ^+$ can be described in terms of forking in $λ$.
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