Specializing Aronszajn trees by countable approximations

Specializing Wide Aronszajn Trees without Adding Reals

We show that under certain circumstances wide Aronszajn trees can be specialized iteratively without adding reals. We then use this fact to study forcing axioms compatible with CH and list some open problems.

Club Stationary Reflection and the Special Aronszajn Tree Property

We prove that it is consistent that Club Stationary Reflection and the Special Aronszajn Tree Property simultaneously hold on $ω_2$, thereby contributing to the study of the tension between compactness and incompactness in set theory. The poset which produces the final model follows the collapse of an ineffable cardinal first with an iteration of club adding (with anticipation) and second with an iteration specializing Aronszajn trees. In the first part of the paper, we prove a general theorem about specializing Aronszajn trees on $ω_2$ after forcing with what we call $\mathcal{F}$-Strongly Pr…

不可数线性序的一个虚拟五元基

A virtual five element basis for the uncountable linear orders

该研究通过证明Aronzsajn线与Countryman线的同构嵌入结论，结合真力迫等新保持性结果，解答了不可数线性序五元基存在性等相关数理逻辑问题，推广了前人工作。

Can a small forcing create Kurepa trees?

In the paper we probe the possibilities of creating a Kurepa tree in a generic extension of a model of CH plus no Kurepa trees by an omega_1-preserving forcing notion of size at most omega_1. In the first section we show that in the Levy model obtained by collapsing all cardinals between omega_1 and a strongly inaccessible cardinal by forcing with a countable support Levy collapsing order many omega_1-preserving forcing notions of size at most omega_1 including all omega-proper forcing notions and some proper but not omega-proper forcing notions of size at most omega_1 do not create Kurepa tre…

从自由 Suslin 树构造一个刚性 Kurepa 树

A Rigid Kurepa Tree From a Free Suslin Tree

本文通过分析自由 Suslin 树的可数支撑积，将其转化为无 Aronszajn 子树的高度刚性 Kurepa 树，并引入了树的新刚性性质。

可逆树与不可逆树

Reversible and Irreversible Trees

本文通过往返系统刻画树的序型可逆性，证明不可逆性等价于存在临界节点或原型子树，并由此给出多类可逆树的存在性与判定条件。