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Synopsis
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 behavior 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 to 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 97 are formulated. Based on "Cardinal Functions on Boolean Algebras (1990)" by the same author, the present work is nearly twice the size of the original work. It contains solutions to many of the open problems which are discussed in greater detail than before. Among the new topics considered are ultraproducts and Fedorchukis theorem, and there is a more complete treatment of the cellularity of free products. Diagrams at the end of the book summarize the relationships between the functions for many important classes of Boolean algebras, including tree algebras and superatomic algebras. Review: 'This book is an indispensable tool for anyone working in Boolean algebra, and is also recommended for set-theoretic topologists' - "Zentralblatt MATH".
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Review
From reviews:
"This book is an indispensable tool for anyone working in Boolean algebra, and is also recommended for set-theoretic topologists." - Zentralblatt MATH
"About this title" may belong to another edition of this title.
- PublisherBirkhäuser
- Publication date2009
- ISBN 10 3034603339
- ISBN 13 9783034603331
- BindingPaperback
- LanguageEnglish
- Edition number1
- Number of pages310
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Covers most of what was known on cardinal invariants in Boolean algebrasList of 97 interesting open problemsSpecial operations on Boolean algebras.- Special classes of Boolean algebras.- Cellularity.- Depth.- Topological density.- ?-weight. Seller Inventory # 4317924
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