Weakly almost periodic functions, model-theoretic stability, and minimality of topological groups
Weakly almost periodic functions, model-theoretic stability, and minimality of topological groups
复制标题
弱几乎周期函数、模型理论稳定性和拓扑群的极小性
DOI：
--
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
T. Tsankov
中科院分区：
文献类型：
--
作者：
I. Yaacov;T. Tsankov
我们研究了$Aleph_0$-范畴结构的自同构群，证明了它们正是Roelcke准紧Polish群。证明了结构理论稳定的充要条件是自同构群上的每个Roelcke一致连续函数都是弱概周期函数。对弱概周期紧化的半群结构进行了分析，证明了从稳定的Aleph_0范畴结构的自同构群到Hausdorff拓扑群的连续满射同态是开的。我们还产生了一些新的WAP-平凡群，并计算了一些例子中的WAP紧化。
We investigate the automorphism groups of $aleph_0$-categorical structures and prove that they are exactly the Roelcke precompact Polish groups. We show that the theory of a structure is stable if and only if every Roelcke uniformly continuous function on the automorphism group is weakly almost periodic. Analysing the semigroup structure on the weakly almost periodic compactification, we show that continuous surjective homomorphisms from automorphism groups of stable $aleph_0$-categorical structures to Hausdorff topological groups are open. We also produce some new WAP-trivial groups and calculate the WAP compactification in a number of examples.