Orthogonality and domination in unstable theories

有序群的o-极小扩张中的正交性与支配关系

Orthogonality and domination in o-minimal expansions of ordered groups

本文分析了有序群o-极小扩张中不变类型的支配关系，证明支配偏序集分解为实闭域o-极小扩张与线性o-极小结构的偏序集直积，并利用短闭包预几何证明可定义类型支配等价于1-类型积，依全局域可定义性分为两类或四类。

Stable domination and independence in algebraically closed valued fields

We seek to create tools for a model-theoretic analysis of types in algebraically closed valued fields (ACVF). We give evidence to show that a notion of 'domination by stable part' plays a key role. In Part A, we develop a general theory of stably dominated types, showing they enjoy an excellent independence theory, as well as a theory of definable types and germs of definable functions. In Part B, we show that the general theory applies to ACVF. Over a sufficiently rich base, we show that every type is stably dominated over its image in the value group. For invariant types over any base, stabl…