04241nam 22006495 450 991036495730332120200630004356.03-030-27093-910.1007/978-3-030-27093-3(CKB)4100000010011850(MiAaPQ)EBC6001357(DE-He213)978-3-030-27093-3(PPN)242818684(EXLCZ)99410000001001185020191224d2019 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierCombinatorial Set Theory of C*-algebras /by Ilijas Farah1st ed. 2019.Cham :Springer International Publishing :Imprint: Springer,2019.1 online resource (535 pages)Springer Monographs in Mathematics,1439-73823-030-27091-2 Includes bibliographical references and index.1. C*-algebras, Abstract and Concrete -- 2. Examples and Constructions of C*-algebras -- 3. Representations of C*-algebras -- 4. Tracial States and Representations of C*-algebras -- 5. Irreducible Representations of C*-algebras -- Part II Set Theory and Nonseparable C*-algebras -- 6. Infinitary Combinatorics, I -- 7. Infinitary Combinatorics, II: The Metric Case -- 8. Additional Set-Theoretic Axioms -- 9. Set Theory and Quotients -- 10. Constructions of Nonseparable C*-algebras, I: Graph CCR Algebras -- 11. Constructions of Nonseparable C*-algebras, II -- Part III Massive Quotient C*-algebras -- 12. The Calkin Algebra -- 13. Multiplier Algebras and Coronas -- 14. Gaps and Incompactness -- 15. Degree-1 Saturation -- 16. Full Saturation -- 17. Automorphisms of Massive Quotient C*-Algebras.-Part IV Appendices -- A. Axiomatic Set Theory -- B. Descriptive Set Theory -- C. Functional Analysis -- D. Model Theory -- References -- Index -- List of Symbols.This book explores and highlights the fertile interaction between logic and operator algebras, which in recent years has led to the resolution of several long-standing open problems on C*-algebras. The interplay between logic and operator algebras (C*-algebras, in particular) is relatively young and the author is at the forefront of this interaction. The deep level of scholarship contained in these pages is evident and opens doors to operator algebraists interested in learning about the set-theoretic methods relevant to their field, as well as to set-theorists interested in expanding their view to the non-commutative realm of operator algebras. Enough background is included from both subjects to make the book a convenient, self-contained source for students. A fair number of the exercises form an integral part of the text. They are chosen to widen and deepen the material from the corresponding chapters. Some other exercises serve as a warmup for the latter chapters.Springer Monographs in Mathematics,1439-7382Mathematical logicFunctional analysisOperator theoryAssociative ringsRings (Algebra)Mathematical Logic and Foundationshttps://scigraph.springernature.com/ontologies/product-market-codes/M24005Functional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Operator Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M12139Associative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11027Mathematical logic.Functional analysis.Operator theory.Associative rings.Rings (Algebra).Mathematical Logic and Foundations.Functional Analysis.Operator Theory.Associative Rings and Algebras.512.55Farah Ilijasauthttp://id.loc.gov/vocabulary/relators/aut781294MiAaPQMiAaPQMiAaPQBOOK9910364957303321-algebras4175437UNINA