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005 20160302172530.0
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020 _a9783034807302
_9978-3-0348-0730-2
024 7 _a10.1007/978-3-0348-0730-2
_2doi
050 4 _aQA8.9-10.3
072 7 _aPBC
_2bicssc
072 7 _aPBCD
_2bicssc
072 7 _aMAT018000
_2bisacsh
082 0 4 _a511.3
_223
100 1 _aMonk, J. Donald.
_eauthor.
245 1 0 _aCardinal Invariants on Boolean Algebras
_h[electronic resource] :
_bSecond Revised Edition /
_cby J. Donald Monk.
250 _a2nd ed. 2014.
264 1 _aBasel :
_bSpringer Basel :
_bImprint: Birkh�user,
_c2014.
300 _aVII, 573 p. 15 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProgress in Mathematics,
_x0743-1643 ;
_v142
505 0 _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 Lindel�f 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.
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.
650 0 _aMathematics.
650 0 _aAlgebra.
650 0 _aOrdered algebraic structures.
650 0 _aMathematical logic.
650 1 4 _aMathematics.
650 2 4 _aMathematical Logic and Foundations.
650 2 4 _aOrder, Lattices, Ordered Algebraic Structures.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783034807296
830 0 _aProgress in Mathematics,
_x0743-1643 ;
_v142
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-0348-0730-2
912 _aZDB-2-SMA
999 _c206179
_d206179