论文标题
在弱O最小非估计结构中可定义的组
Groups definable in weakly o-minimal non-valuational structures
论文作者
论文摘要
令$ \ Mathcal m $为弱的O-Waruation non-dyaluation结构，而$ \ Mathcal n $其规范O-Minimal扩展（由Wencel）。我们证明，$ \ Mathcal m $中的每个组$ g $都是$ \ natcal n $中$ k $的子组，从某种意义上说，这是最小的组。作为一个应用程序，我们获得了$ g^{00} = g \ cap k^{00} $，并在这种情况下建立Pillay的猜想：配备逻辑拓扑的$ g/g/g/g^{00} $是紧凑的谎言组，是一个紧凑的谎言组，如果$ g $具有非常满意的通用，则是$ \ dim_ dim_ lie_ lie_ lie_ lim_ c^lim} $ {
Let $\mathcal M$ be a weakly o-minimal non-valuational structure, and $\mathcal N$ its canonical o-minimal extension (by Wencel). We prove that every group $G$ definable in $\mathcal M$ is a subgroup of a group $K$ definable in $\mathcal N$, which is canonical in the sense that it is the smallest such group. As an application, we obtain that $G^{00}= G\cap K^{00}$, and establish Pillay's Conjecture in this setting: $G/G^{00}$, equipped with the logic topology, is a compact Lie group, and if $G$ has finitely satisfiable generics, then $\dim_{Lie}(G/G^{00})= \dim(G)$.
