Cardinal Invariants on Boolean Algebras. Modern Birkhäuser Classics (eBook)

James D. Monk (Autor)

eBook Download: PDF

2009 | 1. Auflage
IX, 304 Seiten
Birkhäuser Basel (Verlag)
978-3-0346-0334-8 (ISBN)

Infos

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 to 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 97 are formulated. Based on Cardinal Functions on Boolean Algebras (1990) by the same author, the present work is nearly twice the size of the original work. It contains solutions to many of the open problems which are discussed in greater detail than before. Among the new topics considered are ultraproducts and Fedorchukís theorem, and there is a more complete treatment of the cellularity of free products. Diagrams at the end of the book summarize the relationships between the functions for many important classes of Boolean algebras, including tree algebras and superatomic algebras. Review: "This book is an indispensable tool for anyone working in Boolean algebra, and is also recommended for set-theoretic topologists." - Zentralblatt MATH TOC: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 Lindelöf degree.- Hereditary density.- Incomparability.- Hereditary cofinality.- Number of ultrafilters, automorphisms, endomorphisms, ideals, subalgebras.- Other cardinal functions.- Diagrams.- Examples.

Inhalt

Foreword 7
Table of contents 8
0. Introduction 9
1. Special operations on Boolean algebras 17
2. Special classes of Boolean algebras 33
3. Cellularity 53
4. Depth 94
5. Topological density 115
6. p-weight 124
7. Length 133
8. Irredundance 141
9. Cardinality 153
10. Independence 155
11. p-Character 162
12. Tightness 172
13. Spread 183
14. Character 189
15. Hereditary Lindelöf degree 198
16. Hereditary density 204
17. Incomparability 226
18. Hereditary cofinality 234
19. Number of ultrafilters 240
20. Number of automorphisms 241
21. Number of endomorphisms 244
22. Number of ideals 246
23. Number of subalgebras 247
24. Other cardinal functions 252
25. Diagrams 256
26. Examples 279
References 286
Index of problems 293
Index of symbols 299
Index of names and words 301

Produkt-Details

• Erscheint lt. Verlag: 1.1.2009
• Sprache: englisch
• Original-Titel: 978-3-7643-5402-2 (PM)
• Themenwelt: Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Technik
• Schlagworte: Boolean algebra • Cardinal functions • Cellularity • Fedorchukís theorem • forcing • Logic • Proof • set theory • Ultraproduct
• ISBN-10: 3-0346-0334-7 / 3034603347
• ISBN-13: 978-3-0346-0334-8 / 9783034603348