Questions on cardinal invariants of Boolean algebras

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.

Automated summary

The book "Cardinal Invariants on Boolean Algebras" by J. Donald Monk defines and studies many cardinal functions, some of which are generalizations of well-known cardinal characteristics of the continuum. The book also presents a long list of open problems. This study provides definitive answers to several of these problems, focusing on a few cardinal invariants. These problems can be divided into two groups, one concerning the change in cardinal functions when moving from a given infinite Boolean algebra to its simple extensions, and the other comparing a couple of given infinite Boolean algebras and their free product.