强反射性质与Harrington原理

全局$Σ^1_{n+1}$-一致化性质与$\boldsymbol{\textsf{BPFA}}$

The global $Σ^1_{n+1}$-Uniformization Property and $\mathsf{BPFA}$

该研究在数理逻辑领域，证明利用反射基数可构造满足$\textsf{BPFA}$且对所有$n≥2$同时成立$Σ^1_n$-一致化性质的模型。

关于\aleph_1上可定义树性质的一致性

On the consistency of the definable tree property on \aleph_1

本文证明了“H_{omega_1}上一阶可定义的每一棵ω_1树都有一个共尾分支”的等同性，且存在一个Pi^1_1反射基数.证明使用了一个关于aleph_1的拉姆齐定理的可定义版本，该定理再次与Pi^1_1反射基数等相容。我们还证明了除了$MA$的可定义树属性增加的一致性强度的弱紧基数。最后，我们评论推广到更高的基数。

The consistency strength of the perfect set property for universally Baire sets of reals

We show that the statement "every universally Baire set of reals has the perfect set property" is equiconsistent modulo ZFC with the existence of a cardinal that we call a virtually Shelah cardinal. These cardinals resemble Shelah cardinals but are much weaker: if $0^\sharp$ exists then every Silver indiscernible is virtually Shelah in $L$. We also show that the statement $\text{uB} = {\bfΔ}^1_2$, where $\text{uB}$ is the pointclass of all universally Baire sets of reals, is equiconsistent modulo ZFC with the existence of a $Σ_2$-reflecting virtually Shelah cardinal.