MODEL THEORY, KEISLER MEASURES AND GROUPS

This paper continues to study stable-like phenomena in NIP theories. Based on the previous work of Shelah and Poizat, the important role of forking and invariant types in NIP is demonstrated by establishing counterparts of some results for global types from the stable case. In particular, the distinction between type-definable and invariant objects of bounded index is brought into the picture, and it is shown that Lascar strong types coincide with Kim-Pillay strong types over extension bases. The theory is demonstrated to be particularly strong in the case of generically stable types . These types generalize stably dominated types that played a crucial role in the study of algebraically closed valued fields by Haskell, Hrushovski and Macpherson, and have many equivalent characterizations in terms of forking. systematic types theories. non-forking products via

本文继续研究NIP理论中的类似稳定现象。基于Shelah和Poizat先前的工作，通过建立稳定情形下一些关于全局型结果的对应物，展示了分叉和不变型在NIP中的重要作用。特别地，有界指标的型可定义对象和不变对象之间的区别被引入，并且表明在扩张基上，拉斯卡尔强型与金 - 皮莱强型一致。在一般稳定型的情形下，该理论被证明是特别强大的。这些型推广了在哈斯克尔、赫鲁绍夫斯基和麦克弗森对代数闭赋值域的研究中起关键作用的稳定支配型，并且在分叉方面有许多等价的刻画。系统型理论。通过非分叉积