More Jonsson algebras

Jónsson-Tarski表示的扩展及谓词非正规模态逻辑中的模型存在性

An extension of Jónsson-Tarski representation and model existence in predicate non-normal modal logics

本文扩展了Jónsson-Tarski表示定理以保留可数无穷交与并，利用邻域框架和Q-滤子证明了正规与非正规谓词模态逻辑在常数域邻域框架上的模型存在性及完全性。

不同基数的Jónsson群

Jónsson groups of various cardinalities

本文利用Obraztsov嵌入定理，证明无穷基数κ存在Jónsson群当且仅当存在同基数Jónsson代数，将Jónsson群的存在性问题归约为已研究的Jónsson基数问题，推出任意大基数Jónsson群存在且Babai无穷边轨道猜想成立。

包含Thompson群的 relation algebras

Relation algebras containing Thompson groups

本文回顾了Tarski relation algebras与Thompson群的联系，证明了包含特定共轭quasiprojections的代数包含这些群的同态像，并将tabular relation algebras的可表示性扩展至J-algebras。

Strongly compact cardinals and ordinal definability

This paper explores several topics related to Woodin's HOD conjecture. We improve the large cardinal hypothesis of Woodin's HOD dichotomy theorem from an extendible cardinal to a strongly compact cardinal. We show that assuming there is a strongly compact cardinal and the HOD hypothesis holds, there is no elementary embedding from HOD to HOD, settling a question of Woodin. We show that the HOD hypothesis is equivalent to a uniqueness property of elementary embeddings of levels of the cumulative hierarchy. We prove that the HOD hypothesis holds if and only if every regular cardinal above the fi…

布尔代数上模态算子和时态算子的结构

On the structure of modal and tense operators on a boolean algebra

本文研究布尔代数上必然、可能及时态算子的偏序集结构，证明其并半格性质及完备条件下的frame性质，并利用Jonsson-Tarski对偶性刻画对应关系。

可表示的分配准关系代数

Representable distributive quasi relation algebras

本文为分配准关系代数提出可表示性定义，通过偏序等价关系的上集格构造并施加对称性要求，推广了经典关系代数可表示性理论，给出例子和有限可表示的必要条件，并提出若干开放问题。