Cardinal Invariants on Boolean Algebras
Seiten
2009
|
1st ed. 1996. 2nd printing 2009
Springer Basel (Verlag)
978-3-0346-0333-1 (ISBN)
Springer Basel (Verlag)
978-3-0346-0333-1 (ISBN)
This text covers cardinal number valued functions defined for any Boolean algebra such as cellularity. It explores the behavior of these functions under algebraic operations such as products, free products, ultraproducts and their relationships to each other.
This is a greatly revised and expanded version of the book Cardinal fu- tionsonBooleanalgebras,Birkh auser1990.Knownmistakesinthatbookhave beencorrected,andmanyoftheproblemsstatedtherehavesolutionsinthepresent treatment. At the same time, many new problems are formulated here; some as development of the solved problems from the earlier work, but most as a result of more careful study of the notions. The book is supposed to be self-contained, and for that reason many classical results are included. ForhelponthisbookIwishtothankE.K.vanDouwen,K.Grant,L. Heindorf, I. Juh asz, S. Koppelberg, P. Koszmider, P. Nyikos, D. Peterson, M. Rubin, S. Shelah, and S. Todor? cevi c. Unpublished results of some of these people are contained here, sometimes with proofs, with their permission. As the reader will see, my greatest debt is to Saharon Shelah, who has worked on, and solved, many of the problems stated in the 1990 book as well as in preliminary versions of this book. Of course I am always eager to hear about solutions of problems, mistakes, etc. Electronic lists of errata and the status of the open problems are maintained, initially on the anonymous ftp server of euclid.colorado.edu, directory pub/babib; on www, go to ftp://euclid.colorado.edu/pub/babib.
This is a greatly revised and expanded version of the book Cardinal fu- tionsonBooleanalgebras,Birkh auser1990.Knownmistakesinthatbookhave beencorrected,andmanyoftheproblemsstatedtherehavesolutionsinthepresent treatment. At the same time, many new problems are formulated here; some as development of the solved problems from the earlier work, but most as a result of more careful study of the notions. The book is supposed to be self-contained, and for that reason many classical results are included. ForhelponthisbookIwishtothankE.K.vanDouwen,K.Grant,L. Heindorf, I. Juh asz, S. Koppelberg, P. Koszmider, P. Nyikos, D. Peterson, M. Rubin, S. Shelah, and S. Todor? cevi c. Unpublished results of some of these people are contained here, sometimes with proofs, with their permission. As the reader will see, my greatest debt is to Saharon Shelah, who has worked on, and solved, many of the problems stated in the 1990 book as well as in preliminary versions of this book. Of course I am always eager to hear about solutions of problems, mistakes, etc. Electronic lists of errata and the status of the open problems are maintained, initially on the anonymous ftp server of euclid.colorado.edu, directory pub/babib; on www, go to ftp://euclid.colorado.edu/pub/babib.
Special operations on Boolean algebras.- Special classes of Boolean algebras.- Cellularity.- Depth.- Topological density.- ?-weight.- Length.- Irredundance.- Cardinality.- Independence.- ?-Character.- Tightness.- Spread.- Character.- Hereditary Lindelöf 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.
From reviews:
"This book is an indispensable tool for anyone working in Boolean algebra, and is also recommended for set-theoretic topologists." - Zentralblatt MATH
| Erscheint lt. Verlag | 26.11.2009 |
|---|---|
| Reihe/Serie | Modern Birkhäuser Classics |
| Zusatzinfo | IX, 301 p. |
| Verlagsort | Basel |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 462 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
| Mathematik / Informatik ► Mathematik ► Algebra | |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| Schlagworte | Boolean algebra • Boolesche Algebra • Cardinal functions • Cellularity • Fedorchukis theorem • Fedorchukís theorem • forcing • Hardcover, Softcover / Mathematik/Grundlagen • Logic • Proof • set theory • Ultraproduct |
| ISBN-10 | 3-0346-0333-9 / 3034603339 |
| ISBN-13 | 978-3-0346-0333-1 / 9783034603331 |
| Zustand | Neuware |
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