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000696985 0247_ $$a10.1007/978-3-0348-0730-2$$2doi
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000696985 035__ $$aSP(OCoLC)870899132$$z(OCoLC)870766622
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000696985 1001_ $$aMonk, J. Donald$$q(James Donald),$$d1930-$$eauthor.
000696985 24510 $$aCardinal invariants on Boolean algebras$$h[electronic resource]  /$$cJ. Donald Monk.
000696985 250__ $$aSecond revised edition.
000696985 264_1 $$aBasel :$$bBirkhäuser,$$c2014.
000696985 300__ $$a1 online resource.
000696985 336__ $$atext$$btxt$$2rdacontent
000696985 337__ $$acomputer$$bc$$2rdamedia
000696985 338__ $$aonline resource$$bcr$$2rdacarrier
000696985 4901_ $$aProgress in mathematics ;$$vvolume 142
000696985 504__ $$aIncludes bibliographical references and index.
000696985 5050_ $$aIntroduction -- 1. Special Operations on Boolean Algebras -- 2. Special Classes of Boolean Algebras -- 3. Cellularity -- 4. Depth -- 5. Topological Density -- 6. Pi-Weight -- 7. Length -- 8. Irredundance -- 9. Cardinality -- 10. Independence -- 11. Pi-Character -- 12. Tightness -- 13. Spread -- 14. Character -- 15. Hereditary Lindelf Degree -- 16. Hereditary Density -- 17. Incomparability -- 18. Hereditary Cofinality -- 19. Number of Ultrafilters -- 20. Number of Automorphisms -- 21. Number of Endomorphisms -- 22. Number of Ideals -- 23. Number of Subalgebras -- 24. Other Cardinal Functions -- 25. Diagrams -- 26. Examples -- 27. Problems .
000696985 506__ $$aAccess limited to authorized users.
000696985 520__ $$aThis book is concerned with cardinal number valued functions defined for any Boolean algebra. Examples of such functions are independence, which assigns to each Boolean algebra the supremum of the cardinalities of its free subalgebras, and cellularity, which gives the supremum of cardinalities of sets of pairwise disjoint elements. Twenty-one such functions are studied in detail, and many more in passing. The questions considered are the behaviour of these functions under algebraic operations such as products, free products, ultraproducts, and their relationships to one another. Assuming familiarity with only the basics of Boolean algebras and set theory, through simple infinite combinatorics and forcing, the book reviews current knowledge about these functions, giving complete proofs for most facts. A special feature of the book is the attention given to open problems, of which 185 are formulated. Based on Cardinal Functions on Boolean Algebras (1990) and Cardinal Invariants on Boolean Algebras (1996) by the same author, the present work is much larger than either of these. It contains solutions to many of the open problems of the earlier volumes. Among the new topics are continuum cardinals on Boolean algebras, with a lengthy treatment of the reaping number. Diagrams at the end of the book summarize the relationships between the functions for many important classes of Boolean algebras, including interval algebras, tree algebras and superatomic algebras.
000696985 588__ $$aDescription based on print version record.
000696985 650_0 $$aAlgebra, Boolean.
000696985 650_0 $$aFunctions.
000696985 650_0 $$aCardinal numbers.
000696985 77608 $$iPrint version:$$aMonk, J. Donald (James Donald), 1930- author.$$tCardinal invariants on Boolean algebras.$$bSecond edition$$z9783034807296$$w(OCoLC)863174330
000696985 830_0 $$aProgress in mathematics (Boston, Mass.) ;$$vv.142.
000696985 85280 $$bebk$$hSpringerLink
000696985 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-0348-0730-2$$zOnline Access
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000696985 983__ $$aOnline
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