This text covers cardinal number valued functions defined for any Boolean algebra such as cellularity. It explores the behavior of these functions under algebraic operations such as products, free products, ultraproducts and their relationships to each other.

This book is concerned with cardinal number valued functions defined for any Boolean algebra. Examples of such functions are independence, which assigns to each Boolean algebra the supremum of the cardinalities of its free subalgebras, and cellularity, which gives the supremum of cardinalities of sets of pairwise disjoint elements. Twenty-one such functions are studied in detail, and many more in passing. The questions considered are the behaviour of these functions under algebraic operations such as products, free products, ultraproducts, and their relationships to one another. Assuming familiarity with only the basics of Boolean algebras and set theory, through simple infinite combinatorics and forcing, the book reviews current knowledge about these functions, giving complete proofs for most facts. A special feature of the book is the attention given to open problems, of which 185 are formulated. Based on Cardinal Functions on Boolean Algebras (1990) and Cardinal Invariants on Boolean Algebras (1996) by the same author, the present work is much larger than either of these. It contains solutions to many of the open problems of the earlier volumes. Among the new topics are continuum cardinals on Boolean algebras, with a lengthy treatment of the reaping number. Diagrams at the end of the book summarize the relationships between the functions for many important classes of Boolean algebras, including interval algebras, tree algebras and superatomic algebras.

Boolean Algebras in Analysis consists of two parts. The first concerns the general theory at the beginner's level. Presenting classical theorems, the book describes the topologies and uniform structures of Boolean algebras, the basics of complete Boolean algebras and their continuous homomorphisms, as well as lifting theory. The first part also includes an introductory chapter describing the elementary to the theory. The second part deals at a graduate level with the metric theory of Boolean algebras at a graduate level. The covered topics include measure algebras, their sub algebras, and groups of automorphisms. Ample room is allotted to the new classification theorems abstracting the celebrated counterparts by D.Maharam, A.H. Kolmogorov, and V.A.Rokhlin. Boolean Algebras in Analysis is an exceptional definitive source on Boolean algebra as applied to functional analysis and probability. It is intended for all who are interested in new and powerful tools for hard and soft mathematical analysis.

Convenient access to information from every area of mathematics: Fourier transforms, Z transforms, linear and nonlinear programming, calculus of variations, random-process theory, special functions, combinatorial analysis, game theory, much more.

Concise text begins with overview of elementary mathematical concepts and outlines theory of Boolean algebras; defines operators for elimination, division, and expansion; covers syllogistic reasoning, solution of Boolean equations, functional deduction. 1990 edition.

This Handbook is an introduction to set-theoretic topology for students in the field and for researchers in other areas for whom results in set-theoretic topology may be relevant. The aim of the editors has been to make it as self-contained as possible without repeating material which can easily be found in standard texts. The Handbook contains detailed proofs of core results, and references to the literature for peripheral results where space was insufficient. Included are many open problems of current interest.In general, the articles may be read in any order. In a few cases they occur in pairs, with the first one giving an elementary treatment of a subject and the second one more advanced results. These pairs are: Hodel and Juhász on cardinal functions; Roitman and Abraham-Todorčević on S- and L-spaces; Weiss and Baumgartner on versions of Martin's axiom; and Vaughan and Stephenson on compactness properties.