The Resource Cardinal Invariants on Boolean Algebras : Second Revised Edition, by J. Donald Monk, (electronic resource)
Cardinal Invariants on Boolean Algebras : Second Revised Edition, by J. Donald Monk, (electronic resource)
Resource Information
The item Cardinal Invariants on Boolean Algebras : Second Revised Edition, by J. Donald Monk, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Cardinal Invariants on Boolean Algebras : Second Revised Edition, by J. Donald Monk, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 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 edition 2014.
 Extent
 VII, 573 pages 15 illustrations
 Contents

 Introduction
 1. Special Operations on Boolean Algebras
 2. Special Classes of Boolean Algebras
 3. Cellularity
 4. Depth
 5. Topological Density
 6. PiWeight
 7. Length
 8. Irredundance
 9. Cardinality
 10. Independence
 11. PiCharacter
 12. Tightness
 13. Spread
 14. Character
 15. Hereditary Lindelöf 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
 References
 Symbol Index
 Subject Index
 Name Index
 Isbn
 9783034807302
 Label
 Cardinal Invariants on Boolean Algebras : Second Revised Edition
 Title
 Cardinal Invariants on Boolean Algebras
 Title remainder
 Second Revised Edition
 Statement of responsibility
 by 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
 ITFiEUI
 http://library.link/vocab/creatorDate
 1930
 http://library.link/vocab/creatorName
 Monk, J. Donald
 Image bit depth
 0
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName
 SpringerLink (Online service)
 Series statement

 Progress in Mathematics,
 Springer eBooks
 Series volume
 142
 http://library.link/vocab/subjectName

 Mathematics
 Algebra
 Logic, Symbolic and mathematical
 Label
 Cardinal Invariants on Boolean Algebras : Second Revised Edition, by J. Donald Monk, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 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. PiWeight  7. Length  8. Irredundance  9. Cardinality  10. Independence  11. PiCharacter  12. Tightness  13. Spread  14. Character  15. Hereditary Lindelöf 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  References  Symbol Index  Subject Index  Name Index
 Control code
 9783034807302
 Dimensions
 unknown
 Edition
 Second edition 2014.
 Extent
 VII, 573 pages 15 illustrations
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783034807302
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9783034807302
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1086470545
 Label
 Cardinal Invariants on Boolean Algebras : Second Revised Edition, by J. Donald Monk, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 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. PiWeight  7. Length  8. Irredundance  9. Cardinality  10. Independence  11. PiCharacter  12. Tightness  13. Spread  14. Character  15. Hereditary Lindelöf 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  References  Symbol Index  Subject Index  Name Index
 Control code
 9783034807302
 Dimensions
 unknown
 Edition
 Second edition 2014.
 Extent
 VII, 573 pages 15 illustrations
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783034807302
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9783034807302
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1086470545
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/CardinalInvariantsonBooleanAlgebrasSecond/g4A0c2fMwz0/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/CardinalInvariantsonBooleanAlgebrasSecond/g4A0c2fMwz0/">Cardinal Invariants on Boolean Algebras : Second Revised Edition, by J. Donald Monk, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>