Description 
1 online resource 
Series 
Progress in mathematics ; volume 142 

Progress in mathematics (Boston, Mass.) ; v. 142

Contents 
Introduction  1. Special Operations on Boolean Algebras  2. Special Classes of Boolean Algebras  3. Cellularity  4. Depth  5. Topological Density  6. PiWeight  7. Length  8. Irredundance  9. Cardinality  10. Independence  11. PiCharacter  12. Tightness  13. Spread  14. Character  15. Hereditary Lindelf Degree  16. Hereditary Density  17. Incomparability  18. Hereditary Cofinality  19. Number of Ultrafilters  20. Number of Automorphisms  21. Number of Endomorphisms  22. Number of Ideals  23. Number of Subalgebras  24. Other Cardinal Functions  25. Diagrams  26. Examples  27. Problems 
Summary 
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. Twentyone 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 
Bibliography 
Includes bibliographical references and index 
Notes 
Print version record 
Subject 
Algebra, Boolean.


Functions.


Cardinal numbers.

Form 
Electronic book

ISBN 
3034807309 (electronic book) 

9783034807302 (electronic book) 
