论文标题
非Archimedean TSI抛光群及其潜在的Borel复杂性光谱
Non-Archimedean TSI Polish groups and their potential Borel complexity spectrum
论文作者
论文摘要
Scott对可数结构的分析的变化应用于不断作用在波兰空间上的非架构的TSI波兰人群体的作用。我们给出了此类组潜在的Borel复杂性谱的结果，并定义了每个Borel复杂性类别的通用轨道等效关系。我们还确定了此类群体的行动对分类性的障碍，即相对于$ e_ \ infty $，我们适用于Clemens-Coskey的跳跃，可计数可数的骨质等效关系。最后，我们表征了等效关系，这些关系既可以还原为$ =^+$，又可以由非架构的tsi polish组分类，从而扩展了ding和gao的结果。在此过程中，在轨道降低的轨道等效关系理论中开发了几种工具，这些工具可能具有独立利益。
A variation of the Scott analysis of countable structures is applied to actions of non-Archimedean TSI Polish groups acting continuously on a Polish spaces. We give results on the potential Borel complexity spectrum of such groups, and define orbit equivalence relations that are universal for each Borel complexity class. We also identify an obstruction to classifiability by actions of such groups, namely generic ergodicity with respect to $E_\infty$, which we apply to Clemens-Coskey jumps of countable Borel equivalence relations. Finally, we characterize the equivalence relations that are both Borel-reducible to $=^+$ and classifiable by non-Archimedean TSI Polish groups, extending a result of Ding and Gao. In the process, several tools are developed in the Borel reducibility theory of orbit equivalence relations which are likely to be of independent interest.
