Progress in Mathematics

Cardinal Invariants on Boolean Algebras

Second Revised Edition

Authors: Monk, J. Donald

  • Covers most of what is known on cardinal invariants in Boolean algebras
  • Includes a list of 185 interesting open problems
  • Detailed study of 21 cardinal number valued functions defined for any Boolean algebra
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About this book

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.

Reviews

“This book surveys the theory of cardinal-valued functions for Boolean algebras … . The book provides an invaluable resource for anyone working in Boolean algebras and can also be interesting for people working in set-theoretic topology or combinatorial set theory.” (Juan Carlos Martínez, Mathematical Reviews, April, 2015)


Table of contents (28 chapters)

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-0348-0730-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-0348-0729-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Cardinal Invariants on Boolean Algebras
Book Subtitle
Second Revised Edition
Authors
Series Title
Progress in Mathematics
Series Volume
142
Copyright
2014
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0730-2
DOI
10.1007/978-3-0348-0730-2
Hardcover ISBN
978-3-0348-0729-6
Series ISSN
0743-1643
Edition Number
2
Number of Pages
VII, 573
Number of Illustrations and Tables
15 b/w illustrations
Additional Information
Originally published as volume 142 in the series: Progress in Mathematics
Topics