交叉约束基定理与划分的乘积

分区通用性与鸽巢基定理

Partition genericity and pigeonhole basis theorems

本文提出分区通用性概念，证明余超免疫集与 Kurtz 随机集均具有该性质，并由此回答 Kjos-Hanssen 和 Liu 的问题，统一推出多个鸽巢基定理。

A note on infinite partitions of free products of Boolean algebras

If $A$ is an infinite Boolean algebra the cardinal invariant $\mathfrak{a}(A)$ is defined as the smallest size of an infinite partition of $A$. The cardinal $\mathfrak{a}(A\oplus B)$, where $A\oplus B$ is the free product of the Boolean algebras $A$ and $B$ (whose dual topological space is the product of the dual topological spaces of $A$ and $B$), is below both $\mathfrak{a}(A)$ and $\mathfrak{a}(B)$. The equality $\mathfrak{a}(A\oplus B)=\min\lbrace\mathfrak{a}(A),\mathfrak{a}(B)\rbrace$ is not known to hold for all infinite Boolean algebras $A$ and $B$. Here some lower bounds of $\mathfrak{…

Inner product space with no ortho-normal basis without choice

We prove in ZF that there is an inner product space, in fact, nicely definable with no orthonormal basis.

关于极化划分关系的等价性

On equivalences of polarized partition relations

本文引入广义强序列乘积概念，并纯组合地证明其存在性与极化划分关系等价。