We achieve several results. First, we develop a variant of the theory of absolute Galois groups in the context of many sorted structures. Second, we provide a method for coding absolute Galois groups of structures, so they can be interpreted in some monster model with an additional predicate. Third, we prove the “Weak Independence Theorem” for pseudo-algebraically closed (PAC) substructures of an ambient structure with no finite cover property (nfcp) and the property $B(3)$. Fourth, we describe Kim-dividing in these PAC substructures and show several results related to the SOP_n hierarchy. Fifth, we characterize the algebraic closure in PAC structures.

我们取得了一些成果。首先，我们在许多排序结构的背景下开发了绝对伽罗瓦群理论的变体。其次，我们提供了一种对结构的绝对伽罗瓦群进行编码的方法，因此可以使用附加谓词在某些怪物模型中解释它们。第三，我们证明了没有有限覆盖属性（nfcp）的环境结构的伪代数封闭（PAC）子结构的“弱独立定理”和属性$乙（3）$。第四，我们描述了这些 PAC 子结构中的 Kim 划分，并展示了与 SOP _n层次结构相关的几个结果。第五，我们描述了 PAC 结构中的代数闭包。