Cardinal invariants on Boolean algebras [electronic resource] / J. Donald Monk.
Monk, J. Donald (James Donald), 1930- author.
2014
QA10.3
Available Online

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Title Cardinal invariants on Boolean algebras [electronic resource] / J. Donald Monk.
Author Monk, J. Donald (James Donald), 1930- author.
Edition Second revised edition.
ISBN 9783034807302 electronic book
3034807309 electronic book
9783034807296
3034807295
DOI https://doi.org/10.1007/978-3-0348-0730-2
Published Basel : Birkhäuser, 2014.
Language English
Description 1 online resource.
Other Standard Identifiers 10.1007/978-3-0348-0730-2 doi
Call Number QA10.3
Dewey Decimal Classification 511.324
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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Description based on print version record.
Series Progress in mathematics (Boston, Mass.) ; v.142.
Available in Other Form Cardinal invariants on Boolean algebras.
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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 .

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