Cardinal invariants on Boolean algebras /

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Bibliographic Details
Author / Creator:	Monk, J. Donald (James Donald), 1930- author.
Edition:	Second revised edition.
Imprint:	Basel : Birkhäuser, 2014.
Description:	1 online resource.
Language:	English
Series:	Progress in mathematics ; volume 142 Progress in mathematics (Boston, Mass.) ; v. 142.
Subject:	Algebra, Boolean. Functions. Cardinal numbers. Algebra, Boolean. Cardinal numbers. Functions.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11083385

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ISBN:	9783034807302 3034807309 9783034807296 3034807295
Notes:	Includes bibliographical references and index. Print version record.
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. 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.
Other form:	Print version: Monk, J. Donald (James Donald), 1930- Cardinal invariants on Boolean algebras. Second edition 9783034807296
Standard no.:	10.1007/978-3-0348-0730-2

Table of Contents:

Introduction
1. Special Operations on Boolean Algebras
2. Special Classes of Boolean Algebras
3. Cellularity
4. Depth
5. Topological Density
6. Pi-Weight
7. Length
8. Irredundance
9. Cardinality
10. Independence
11. Pi-Character
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.

Cardinal invariants on Boolean algebras /

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