04395nam 22006375 450 991030015020332120220616194027.03-0348-0730-910.1007/978-3-0348-0730-2(CKB)3710000000088291(SSID)ssj0001175071(PQKBManifestationID)11977513(PQKBTitleCode)TC0001175071(PQKBWorkID)11116252(PQKB)10395590(MiAaPQ)EBC1697865(DE-He213)978-3-0348-0730-2(PPN)176748733(EXLCZ)99371000000008829120140211d2014 u| 0engurcnu||||||||txtccrCardinal Invariants on Boolean Algebras Second Revised Edition /by J. Donald Monk2nd ed. 2014.Basel :Springer Basel :Imprint: Birkhäuser,2014.1 online resource (569 pages) illustrationsProgress in Mathematics,0743-1643 ;142Bibliographic Level Mode of Issuance: Monograph3-0348-0729-5 Includes bibliographical references and indexes.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 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.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.Progress in Mathematics,0743-1643 ;142Mathematical logicAlgebraOrdered algebraic structuresMathematical Logic and Foundationshttps://scigraph.springernature.com/ontologies/product-market-codes/M24005Order, Lattices, Ordered Algebraic Structureshttps://scigraph.springernature.com/ontologies/product-market-codes/M11124Mathematical logic.Algebra.Ordered algebraic structures.Mathematical Logic and Foundations.Order, Lattices, Ordered Algebraic Structures.511.3511.324Monk J. Donaldauthttp://id.loc.gov/vocabulary/relators/aut35706MiAaPQMiAaPQMiAaPQBOOK9910300150203321Cardinal invariants on boolean algebras375229UNINA