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The Resource Cardinal invariants on Boolean algebras, J. Donald Monk
Cardinal invariants on Boolean algebras, J. Donald Monk
Resource Information
The item Cardinal invariants on Boolean algebras, J. Donald Monk represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Cardinal invariants on Boolean algebras, J. Donald Monk represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 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. Twentyone 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
 Edition
 Second revised edition.
 Extent
 vii, 573 pages
 Contents

 Introduction
 Special Operations on Boolean Algebras
 Special Classes of Boolean Algebras
 Cellularity
 Depth
 Topological Density
 PiWeight
 Length
 Irredundance
 Cardinality
 Independence
 PiCharacter
 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
 Isbn
 9783034807296
 Label
 Cardinal invariants on Boolean algebras
 Title
 Cardinal invariants on Boolean algebras
 Statement of responsibility
 J. Donald Monk
 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. Twentyone 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
 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
 Bibliography note
 Includes bibliographical references (pages 551559) 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  PiWeight  Length  Irredundance  Cardinality  Independence  PiCharacter  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
 Bibliography note
 Includes bibliographical references (pages 551559) 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  PiWeight  Length  Irredundance  Cardinality  Independence  PiCharacter  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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