论文标题
可数关系结构的自动形态群的副本
The poset of copies for automorphism groups of countable relational structures
论文作者
论文摘要
令$ \ mathrm {g} $为对称组$ \ mathfrak s（u）$的子组的所有排列的子组。令$ \ overline {\ mathrm {g}} $为$ u^u $上的函数拓扑中$ \ mathrm {g} $的拓扑结束。我们启动了Poset $ \ Overline {\ Mathrm {g}} [u]的研究：= \ {f [f [u] \ mid f \ in \ In \ intlline {\ mathrm {g}} \} $ \ perline {\ mathrm {g} $的函数图像的函数图像的图像。此设置$ \ OVILLINE {\ MATHRM {g}} [U]集合的子集的$将称为\ emph {copt for} for}组$ \ mathrm {g} $。对称组$ \ mathfrak s（u）$的每个子组$ \ mathrm {g} $的事实证明了一个面额，存在$ \ u $上的同质关系结构$ r $，因此$ \ overline g $ coperline g $是均质结构$ r $的嵌入方式，$ r $ r $ $ \ g y g y grm} $ r $中的$ r $的副本和$ u $ $ u $ of $ u $ to $ u $ to $ u $的一组$ \ overline $ \ overline $ \ cap \ cap \ u $的副本集。
Let $\mathrm{G}$ be a subgroup of the symmetric group $\mathfrak S(U)$ of all permutations of a countable set $U$. Let $\overline{\mathrm{G}}$ be the topological closure of $\mathrm{G}$ in the function topology on $U^U$. We initiate the study of the poset $\overline{\mathrm{G}}[U]:=\{f[U]\mid f\in \overline{\mathrm{G}}\}$ of images of the functions in $\overline{\mathrm{G}}$, being ordered under inclusion. This set $\overline{\mathrm{G}}[U]$ of subsets of the set $U$ will be called the \emph{poset of copies for} the group $\mathrm{G}$. A denomination being justified by the fact that for every subgroup $\mathrm{G}$ of the symmetric group $\mathfrak S(U)$ there exists a homogeneous relational structure $R$ on $U$ such that $\overline G$ is the set of embeddings of the homogeneous structure $R$ into itself and $\overline{\mathrm{G}}[U]$ is the set of copies of $R$ in $R$ and that the set of bijections $\overline G\cap \mathfrak S(U)$ of $U$ to $U$ forms the group of automorphisms of $\mathrm{R}$.
