Borel-amenable Reducibilities for Sets of Reals

Beyond Borel-amenability: scales and superamenable reducibilities

We analyze the degree-structure induced by large reducibilities under the Axiom of Determinacy. This generalizes the analysis of Borel reducibilities given in references [1], [6] and [5] e.g. to the projective levels.

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。

拟传递顺从图中的Borel分数完美匹配

Borel fractional perfect matchings in quasi-transitive amenable graphs

本研究针对拟传递顺从图的Borel分数完美匹配问题，证明了具拟传递顺从分支的局部有限Borel图若有分数完美匹配则必有Borel分数完美匹配，并推导出可数顺从拟传递图的Bernoulli图的对应结论，丰富了Borel组合数学相关结果。

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…

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。

The uniform Gardner conjecture and rounding Borel flows

We study groups which satisfy Gardner's equidecomposition conjecture for uniformly distributed sets. We prove that an amenable group has this property if and only if it does not admit $(\mathbb{Z}/2\mathbb{Z}) *(\mathbb{Z}/2\mathbb{Z})$ as a quotient by a finite subgroup. Our technical contribution is an algorithm for rounding Borel flows for actions of amenable groups.