超越Borel顺从性：标度和超顺从可归约性

Baire 归约与良好的 Borel 归约

Baire reductions and good Borel reducibilities

本文证明了由良好 Borel 归约导出的度结构的二分法定理，扩展了文献[8]的结果，使其能处理包括 Baire 类 $ξ$ 函数在内的更大类归约概念。

实数集的Borel顺从可约性

Borel-amenable Reducibilities for Sets of Reals

我们表明，如果$\mathcal{F}$是任何“行为良好”的博雷尔函数的子集，我们假设公理的确定性，然后层次的$\pow(\mathbb{R})$诱导的$\mathcal{F}$原来看起来像瓦奇层次（这是特殊情况下，$\mathcal{F}$是一组连续函数）。

一致博雷尔可 amenability

Uniform Borel Amenability

本文基于统一博雷尔可 amenability 概念，证明其等价于随机博雷尔超有限性，并拓展了康尼斯-费尔曼-韦斯定理的加强版本，同时获得测度理论结构结果及不变测度的奥尼斯坦-韦斯型定理。

Wadge-like degrees of Borel bqo-valued functions

We unite two well known generalisations of the Wadge theory. The first one considers more general reducing functions than the continuous functions in the classical case, and the second one extends Wadge reducibility from sets (i.e., $\{0,1\}$-valued functions) to $Q$-valued functions, for a better quasiorder $Q$. In this article, we consider more general reducibilities on the $Q$-valued functions and generalise some results of L. Motto Ros in the first direction and of T. Kihara and A. Montalbán in the second direction: Our main result states that the structure of the $\mathbfΔ^0_α$-degrees of…

超u-可 amenability 和树形等价关系的超有限性

Hyper-u-amenablity and Hyperfiniteness of Treeable Equivalence Relations

本文研究了可数 Borel 等价关系的超有限性，证明了树形、超 u-可 amenable 等价关系的超有限性，并探讨了相关条件下的等价关系性质。

Isometry group of Borel randomizations

We study global dynamical properties of the isometry group of the Borel randomization of a separable complete structure. In particular, we show that if properties such as the Rohklin property, topometric generics, extreme amenability hold for the isometry group of the structure, they also hold in the isometry group of the randomization.