We introduce the notion of a semi-retraction. Given two structures $\mathcal{A}$ and $\mathcal{B}$, $\mathcal{A}$ is a semi-retraction of $\mathcal{B}$ if there exist quantifier-free type respecting maps $f:\mathcal{B}\to \mathcal{A}$ and $g:\mathcal{A}\to \mathcal{B}$ such that $f\circ g$ is an embedding. We say that a structure has the Ramsey property if its age does. Given two locally finite ordered structures $\mathcal{A}$ and $\mathcal{B}$, if $\mathcal{A}$ is a semi-retraction of $\mathcal{B}$ and $\mathcal{B}$ has the Ramsey property, then $\mathcal{A}$ also has the Ramsey property. We introduce notation for what we call semi-direct product structures, after the group construction known to preserve the Ramsey property [11]. We introduce the notion of a color-homogenizing map, and use this notion to give a finitary argument that the semi-direct product structure of ordered relational structures with the Ramsey property must also have the Ramsey property. Finally, we characterize NIP theories using a generalized indiscernible sequence indexed by a semi-direct product structure.

我们介绍了半缩回的概念。给定两种结构$\mathcal{一种}$ 和 $\mathcal{乙}$， $\mathcal{一种}$ 是半缩回 $\mathcal{乙}$ 是否存在无量词的类型对应图 $F：\mathcal{乙}\to \mathcal{一种}$ 和 $G：\mathcal{一种}\to \mathcal{乙}$ 这样 $F\circ G$是一个嵌入。我们说一个结构如果具有年龄则具有Ramsey属性。给定两个局部有限的有序结构$\mathcal{一种}$ 和 $\mathcal{乙}$如果 $\mathcal{一种}$ 是半缩回 $\mathcal{乙}$ 和 $\mathcal{乙}$ 拥有Ramsey属性，那么 $\mathcal{一种}$也有Ramsey属性。在已知保留Ramsey属性的组构造之后，我们引入称为半直接产品结构的符号[11]。我们介绍了颜色均匀化图的概念，并使用此概念给出了一个明确的论点，即具有Ramsey属性的有序关系结构的半直接乘积结构也必须具有Ramsey属性。最后，我们使用由半直接乘积结构索引的广义不可区分序列来刻画NIP理论。