Abstract
AbstractIn 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.
Publisher
Springer Science and Business Media LLC
Reference5 articles.
1. Baumgartner, J.E., Dordal, P.: Adjoining dominating functions. J. Symbol. Logic 50(1), 94–101 (1985)
2. 2, 3;A Blass,2010
3. Brendle, J.: Forcing and the structure of the real line: the Bogotá lectures. Lecture notes (2009)
4. Koppelberg, S.: Handbook of Boolean Algebras. North Holland (1989)
5. Monk, J.D.: Cardinal Invariants on Boolean Algebras, 2nd edn. Birkhauser (2014)