More on regular reduced products

Reduced products of UHF algebras under forcing axioms

If $A_n$ is a sequence of C*-algebras, then the C*-algebra $\prod A_n / \bigoplus A_n$ is called a reduced product. We prove, assuming Todorcevic's Axiom and Martin's Axiom, that every isomorphism between two reduced products of separable, unital UHF algebras must be definable in a strong sense. As a corollary we deduce that two such reduced products $\prod A_n / \bigoplus A_n$ and $\prod B_n / \bigoplus B_n$ are isomorphic if and only if, up to an almost-permutation of $\mathbb{N}$, $A_n$ is isomorphic to $B_n$.

酉群与矩阵代数约化积的迹范数刚性

Trace-norm rigidity for reduced products of unitary groups and matrix algebras

研究有限维酉群和矩阵代数的迹度量约化积间同态，证明酉群相关稳定性变体等，表明乘积形式同构由特定方式诱导，还得到坐标识别及自同构群的刚性与分类结果，矩阵代数在更一般背景下有类似刚性结果。

Reduced products of metric structures: a metric Feferman-Vaught theorem

We extend the classical Feferman-Vaught theorem to logic for metric structures. This implies that the reduced powers of elementarily equivalent structures are elementarily equivalent, and therefore they are isomorphic under the Continuum Hypothesis. We also prove the existence of two separable C*-algebras of the form $\bigoplus_i M_{k(i)}(\mathbb{C})$ such that the assertion that their coronas are isomorphic is independent from ZFC, which gives the first example of genuinely non-commutative coronas of separable C*-algebras with this property.

无自私的简化解折自由积与HNN扩展

Selfless reduced amalgamated free products and HNN extensions

本文研究了C*-代数简化解折自由积中的无自私包含，并提出了一种构建C*-代数HNN扩展的新方法，同时给出了新的无自私示例，扩展了Ueda、Ivanov和de la Harpe-Preaux的结果。