Cardinal invariants on Boolean algebras

Viac o knihe

This book explores cardinal number valued functions for any Boolean algebra, focusing on examples like independence, which determines the supremum of cardinalities of free subalgebras, and cellularity, which identifies the supremum of cardinalities of pairwise disjoint elements. It examines twenty-one such functions in detail and many more briefly, analyzing their behavior under algebraic operations such as products, free products, and ultraproducts, as well as their interrelationships. Designed for readers with a basic understanding of Boolean algebras and set theory, the text employs simple infinite combinatorics and forcing to review current knowledge, providing complete proofs for most results. Notably, it highlights 185 open problems, enhancing its contribution to the field. Building on previous works by the author, this volume is significantly larger and addresses many unresolved issues from earlier texts. New topics include continuum cardinals on Boolean algebras, with an extensive discussion on the reaping number. Diagrams at the conclusion summarize the relationships between functions for key classes of Boolean algebras, such as interval algebras, tree algebras, and superatomic algebras.