Omitting types theorem and its application

我们引入了几个关于树的不可分辨的新概念。根据定义，树是一个有序集(O，&lt；)，使得对于O$中的任何$a元，由a确定的初始段$元{b元在O：B&lt；a元}$是线性有序集。树的一个典型例子是有限$元omega$-序列的集合$袁omega^{&lt；袁omega}$，其顺序关系为$&lt；_{袁Rm ini}$，其中$元eTA&lt；在本研究中，我们研究了语言中的$M$结构中的$M$。其中$O$是一棵树，$A$是一棵树，$A$是$M$中的一个元素，用$袁ETA$标记，也称为树。我们研究了这类树在一般情况下的不可区分性，并将所得结果应用于不稳定理论的研究。其中，我们证明了如果$袁Gamma$(用公式描述的一组条件)具有强子树性质，则$袁Gamma$由强不可分辨树实现。

We introduced several new notions concerning indiscernibility of trees. A tree is by definition an ordered set (O,<) such that, for any $a ￥in O$, the initial segment $￥{b ￥in O: b<a￥}$ determined by a is a linearly ordered set.A typical example of tree is the set $￥omega^{<￥omega}$ of finite $￥omega$-sequences with the order relation $<_{￥rm ini}$, where $￥eta <_{￥rm ini} ￥nu$ means that $￥eta$ is a proper initial segment of $￥nu$.In this study, we worked in some structure $M$ in the language $L$. A subset $A$ of the form $(a_￥eta)_{￥eta ￥in O}$, where $O$ is a tree, and $a_￥eta$ is an element in $M$ labeled by $￥eta$, is also called a tree. We studied the indiscernibility of such trees $A$ in general settings and then applied the obtained results to the study of unstable theories. Among others, we proved that if $￥Gamma$ (a set of conditions described by formulas) has the strong subtree property then $￥Gamma$ is realized by a strongly indiscernible tree.