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The Resource Cardinal invariants on Boolean algebras, J. Donald Monk

Cardinal invariants on Boolean algebras, J. Donald Monk

Creator
Author
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
Language
eng
Work
Publication
Edition
Second revised edition.
Extent
1 online resource
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
Isbn
9783034807302
Instance
Label
Cardinal invariants on Boolean algebras
Title
Cardinal invariants on Boolean algebras
Statement of responsibility
J. Donald Monk
Creator
Author
Subject
Language
eng
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
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorDate
1930-
http://library.link/vocab/creatorName
Monk, J. Donald
Dewey number
511.324
Index
index present
LC call number
QA10.3
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
NLM call number
Online Book
Series statement
Progress in mathematics
Series volume
volume 142
http://library.link/vocab/subjectName
  • Algebra, Boolean
  • Functions
  • Cardinal numbers
  • MATHEMATICS
  • Algebra, Boolean
  • Cardinal numbers
  • Functions
Label
Cardinal invariants on Boolean algebras, J. Donald Monk
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Control code
870899132
Dimensions
unknown
Edition
Second revised edition.
Extent
1 online resource
File format
unknown
Form of item
online
Isbn
9783034807302
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-0348-0730-2
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)870899132
Label
Cardinal invariants on Boolean algebras, J. Donald Monk
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Control code
870899132
Dimensions
unknown
Edition
Second revised edition.
Extent
1 online resource
File format
unknown
Form of item
online
Isbn
9783034807302
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-0348-0730-2
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)870899132

Subject

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