LEADER 04395nam 22006375 450 001 9910300150203321 005 20220616194027.0 010 $a3-0348-0730-9 024 7 $a10.1007/978-3-0348-0730-2 035 $a(CKB)3710000000088291 035 $a(SSID)ssj0001175071 035 $a(PQKBManifestationID)11977513 035 $a(PQKBTitleCode)TC0001175071 035 $a(PQKBWorkID)11116252 035 $a(PQKB)10395590 035 $a(MiAaPQ)EBC1697865 035 $a(DE-He213)978-3-0348-0730-2 035 $a(PPN)176748733 035 $a(EXLCZ)993710000000088291 100 $a20140211d2014 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aCardinal Invariants on Boolean Algebras $eSecond Revised Edition /$fby J. Donald Monk 205 $a2nd ed. 2014. 210 1$aBasel :$cSpringer Basel :$cImprint: Birkhäuser,$d2014. 215 $a1 online resource (569 pages) $cillustrations 225 1 $aProgress in Mathematics,$x0743-1643 ;$v142 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-0348-0729-5 320 $aIncludes bibliographical references and indexes. 327 $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 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. 330 $aThis book is concerned with cardinal number valued functions defined for any Boolean algebra. Examples of such functions are independence, which assigns to each Boolean algebra the supremum of the cardinalities of its free subalgebras, and cellularity, which gives the supremum of cardinalities of sets of pairwise disjoint elements. Twenty-one such functions are studied in detail, and many more in passing. The questions considered are the behaviour of these functions under algebraic operations such as products, free products, ultraproducts, and their relationships to one another. Assuming familiarity with only the basics of Boolean algebras and set theory, through simple infinite combinatorics and forcing, the book reviews current knowledge about these functions, giving complete proofs for most facts. A special feature of the book is the attention given to open problems, of which 185 are formulated. Based on Cardinal Functions on Boolean Algebras (1990) and Cardinal Invariants on Boolean Algebras (1996) by the same author, the present work is much larger than either of these. It contains solutions to many of the open problems of the earlier volumes. Among the new topics are continuum cardinals on Boolean algebras, with a lengthy treatment of the reaping number. Diagrams at the end of the book summarize the relationships between the functions for many important classes of Boolean algebras, including interval algebras, tree algebras and superatomic algebras. 410 0$aProgress in Mathematics,$x0743-1643 ;$v142 606 $aMathematical logic 606 $aAlgebra 606 $aOrdered algebraic structures 606 $aMathematical Logic and Foundations$3https://scigraph.springernature.com/ontologies/product-market-codes/M24005 606 $aOrder, Lattices, Ordered Algebraic Structures$3https://scigraph.springernature.com/ontologies/product-market-codes/M11124 615 0$aMathematical logic. 615 0$aAlgebra. 615 0$aOrdered algebraic structures. 615 14$aMathematical Logic and Foundations. 615 24$aOrder, Lattices, Ordered Algebraic Structures. 676 $a511.3 676 $a511.324 700 $aMonk$b J. Donald$4aut$4http://id.loc.gov/vocabulary/relators/aut$035706 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300150203321 996 $aCardinal invariants on boolean algebras$9375229 997 $aUNINA