Downward categoricity from a successor inside a good frame

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• 作者：Sebastien Vasey ^sebv@cmu.edu
• 关键词：primary ; 03C48 ; secondary ; 03C45 ; 03C52 ; 03C55
• 刊名：Annals of Pure and Applied Logic
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：168
• 期：3
• 页码：651-692
• 全文大小：934 K
• 卷排序：168

文摘

In the setting of abstract elementary classes (AECs) with amalgamation, Shelah has proven a downward categoricity transfer from categoricity in a successor and Grossberg and VanDieren have established an upward transfer assuming in addition a locality property for Galois types that they called tameness.We further investigate categoricity transfers in tame AECs. We use orthogonality calculus to prove a downward transfer from categoricity in a successor in AECs that have a good frame (a forking-like notion for types of singletons) on an interval of cardinals:Theorem 0.1. LetKbe an AEC and let  LS(K)≤λ<θLS(K)≤λ<θbe cardinals. IfKhas a type-full good  [λ,θ][λ,θ]-frame andKis categorical in both λ and  θ+θ+, thenKis categorical in all  μ∈[λ,θ]μ∈[λ,θ].