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

Cardinal invariants on Boolean algebras, J. Donald Monk

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
UKMGB
http://library.link/vocab/creatorDate
1930-
http://library.link/vocab/creatorName
Monk, J. Donald
Illustrations
illustrations
Index
index present
LC call number
QA10.3
LC item number
.M67 2014
Literary form
non fiction
Nature of contents
bibliography
Series statement
Progress in Mathematics
Series volume
Volume 142
http://library.link/vocab/subjectName
  • Algebra, Boolean
  • Functions
  • Cardinal numbers
  • Algebra, Boolean
  • Cardinal numbers
  • Functions
Label
Cardinal invariants on Boolean algebras, J. Donald Monk
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 551-559) and indexes
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Introduction -- Special Operations on Boolean Algebras -- Special Classes of Boolean Algebras -- Cellularity -- Depth -- Topological Density -- Pi-Weight -- Length -- Irredundance -- Cardinality -- Independence -- Pi-Character -- Tightness -- Spread -- Character -- Hereditary Lindelo f Degree -- Hereditary Density -- Incomparability -- Hereditary Cofinality -- Number of Ultrafilters -- Number of Automorphisms -- Number of Endomorphisms -- Number of Ideals -- Number of Subalgebras -- Other Cardinal Functions -- Diagrams -- Examples -- Problems
Dimensions
24 cm.
Edition
Second revised edition.
Extent
vii, 573 pages
Isbn
9783034807296
Isbn Type
(hbk.)
Lccn
2014932538
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
Other physical details
illustrations
System control number
  • (OCoLC)863174330
  • (OCoLC)ocn863174330
Label
Cardinal invariants on Boolean algebras, J. Donald Monk
Publication
Bibliography note
Includes bibliographical references (pages 551-559) and indexes
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Introduction -- Special Operations on Boolean Algebras -- Special Classes of Boolean Algebras -- Cellularity -- Depth -- Topological Density -- Pi-Weight -- Length -- Irredundance -- Cardinality -- Independence -- Pi-Character -- Tightness -- Spread -- Character -- Hereditary Lindelo f Degree -- Hereditary Density -- Incomparability -- Hereditary Cofinality -- Number of Ultrafilters -- Number of Automorphisms -- Number of Endomorphisms -- Number of Ideals -- Number of Subalgebras -- Other Cardinal Functions -- Diagrams -- Examples -- Problems
Dimensions
24 cm.
Edition
Second revised edition.
Extent
vii, 573 pages
Isbn
9783034807296
Isbn Type
(hbk.)
Lccn
2014932538
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
Other physical details
illustrations
System control number
  • (OCoLC)863174330
  • (OCoLC)ocn863174330

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