当部分Borel序可线性化时

树的乘积与交换部分映射的Borel复杂度

Borel complexity for product of trees and commuting partial maps

本文证明树的乘积上的非柱状作用诱导超有限轨道等价关系，并构造交换部分映射生成万有可数Borel等价关系的例子，与已知定理形成对比。

关于 Sacks 猜想的一个注记：嵌入高度为三的偏序比高度为二的偏序更难

A Note on a Conjecture of Sacks: It is Harder to Embed Height Three Partial Orders than Height Two Partial Orders

本文研究 Sacks 猜想，证明大小为连续统的局部可数偏序在高度为二时可嵌入图灵度，但在高度为三时面临困难，并提出一般性障碍解释此差异。

Borel偏序集的Borel链条件

Borel chain conditions of Borel posets

本文在描述性组合学中研究Borel偏序集的链条件分类，证明了存在与经典情形类似但不同于其他Borel组合学对应物的链条件层级。

解析阶关系的线性化

Linearization of analytic order relations

我们证明了如果$\leq$是一个解析偏序，那么任何一个$\leq$都可以扩展为一个（黑体）$Δ^1_2$线性序类似于$2^{<ω_1}$中的反链字典序或嵌入$\leq.$中的某个Borel偏序$\leq_0$给出了解析等价关系的一些推论，例如，如果$E$是$Σ^1_1[z]$等价关系，使得$E_0$不嵌入到$E$中，则通过与在$L[z]$中编码E-不变量Borel集的交集来确定$E$。

泛型的等价性

Equivalence of generics

本文研究集合论模型中泛型滤子间的Borel等价关系复杂性，证明Cohen力迫对应超有限关系的递增并，随机力迫则既非可顺从也非树状。

Metric fixed point theory and partial impredicativity

We show that the Priess-Crampe & Ribenboim fixed point theorem is provable in $\mathsf{RCA}_0$. Furthermore, we show that Caristi's fixed point theorem for both Baire and Borel functions is equivalent to the transfinite leftmost path principle, which falls strictly between $\mathsf{ATR}_0$ and $Π^1_1\mbox{-}\mathsf{CA}_0$. We also exhibit several weakenings of Caristi's theorem that are equivalent to $\mathsf{WKL}_0$ and to $\mathsf{ACA}_0$.

复分析与偏微分方程中的等变Borel提升

Equivariant Borel liftings in complex analysis and PDE

本文研究复分析与偏微分方程中等变Borel提升的存在性，通过Runge逼近定理和Boreltoast理论，证明了分布拉普拉斯算子等的等变Borel逆在自由部分存在。

The classification of countable models of set theory

We study the complexity of the classification problem for countable models of set theory (ZFC). We prove that the classification of arbitrary countable models of ZFC is Borel complete, meaning that it is as complex as it can conceivably be. We then give partial results concerning the classification of countable well-founded models of ZFC.

On the classification of vertex-transitive structures

We consider the classification problem for several classes of countable structures which are "vertex-transitive", meaning that the automorphism group acts transitively on the elements. (This is sometimes called homogeneous.) We show that the classification of countable vertex-transitive digraphs and partial orders are Borel complete. We identify the complexity of the classification of countable vertex-transitive linear orders. Finally we show that the classification of vertex-transitive countable tournaments is properly above $E_0$ in complexity.