In the book Cardinal Invariants on Boolean Algebras by J. Donald Monk many such cardinal functions are defined and studied. Among them several are generalizations of well known cardinal characteristics of the continuum. Alongside a long list of open problems is given. Focusing on half a dozen of those cardinal invariants some of those problems are given an answer here, which in most of the cases is a definitive one. Most of them can be divided in two groups. The problems of the first group ask about the change on those cardinal functions when going from a given infinite Boolean algebra to its simple extensions, while in the second group the comparison is between a couple of given infinite Boolean algebras and their free product.

在 J. Donald Monk 所著的布尔代数基数不变量一书中，定义和研究了许多此类基数函数。其中有几个是众所周知的连续统基本特征的概括。除了一长串未解决的问题外，还给出了一个清单。关注这些基数不变量中的六个，这里给出了其中一些问题的答案，在大多数情况下这是一个确定的答案。他们中的大多数可以分为两组。第一组的问题询问从给定的无限布尔代数到它的简单扩展时这些基数函数的变化，而在第二组中比较给定的无限布尔代数和它们的自由乘积。