零维波兰空间上Wadge层级的一个分类
A classification of the Wadge hierarchies on zero-dimensional Polish spaces
AI总结：
本文用可数序数作为不变量，完全分类了零维波兰空间上的Wadge层级（序同构意义下），并证明该分类问题无Borel判定程序，结果基于对Wadge层级的显式拓扑描述。
摘要：
我们利用（本质上）可数序数作为完全不变量，提供了零维波兰空间上所有可能的Wadge层级在序同构意义下的完全分类。我们还观察到，尽管我们的不变量指派非常简单且仅有$\aleph_1$-多个等价类，上述分类问题从描述集合论的观点来看是相当复杂的：特别是，不存在Borel程序来确定两个零维波兰空间是否具有同构的Wadge层级。所有结果都基于对任意零维波兰空间上Wadge层级的一个完全且显式的描述，该描述依赖于其拓扑性质。
英文摘要：
We provide a complete classification, up to order-isomorphism, of all possible Wadge hierarchies on zero-dimensional Polish spaces using (essentially) countable ordinals as complete invariants. We also observe that although our assignment of invariants is very simple and there are only $\aleph_1$-many equivalence classes, the above classification problem is quite complex from the descriptive set-theoretic point of view: in particular, there is no Borel procedure to determine whether two zero-dimensional Polish spaces have isomorphic Wadge hierarchies. All results are based on a complete and explicit description of the Wadge hierarchy on an arbitrary zero-dimensional Polish space, depending on its topological properties.
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