Cardinal invariants on Boolean algebras
by Monk, J. Donald, (James Donald)
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 s…
Read More ↓Title Statements
- Full title :Cardinal invariants on Boolean algebras / J. Donald Monk.
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.
Read More ↓Edition Statements
- Publication Date:2014.
- Edition:Second revised edition
Publication Statements
- Publisher(s):Birkhäuser
- Place of Publication:Basel
- Language:eng
- Publication Date:2014.
Notes
Titre de l'écran-titre (visionné le 8 avril 2014).
The Physical Object
- Description:1 ressource en ligne
Edition Identifiers
- ISBN:9783034807302, 3034807309
- oclc:ocn878022102
- LC Classification:QA10.3
- Dewey Decimal:511.324
Table of Contents
Introduction -- 1. Special Operations on Boolean Algebras -- 2. Special Classes of Boolean Algebras -- 3. Cellularity -- 4. Depth -- 5. Topological Density -- 6. Pi-Weight -- 7. Length -- 8. Irredundance -- 9. Cardinality -- 10. Independence -- 11. Pi-Character -- 12. Tightness -- 13. Spread -- 14. Character -- 15. Hereditary Lindelf 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 .
Read More ↓Subjects
Writers
More from this Series
No reviews yet. Be the first to rate this work.
Related Works
more →
Complex geometry and Lie theory
Functions 11
Functions 11
Examples of interdisciplinary teaching at school
Operator theory and complex analysis
Files & Downloads
-
Cardinal Invariants on Boolean Algebras: Second R…
PDF · 5.4 MB · updated -
Cardinal Invariants on Boolean Algebras: Second R…
PDF · 4.4 MB · updated -
Cardinal Invariants on Boolean Algebras: Second R…
PDF · 3.8 MB · updated
Rate & Review