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Combinatorial Set Theory of C*-algebras

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...

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Bibliographic Details
Main Author: Farah, Ilijas
Format: eBook
Language:English
Published: Cham Springer International Publishing 2019, 2019
Edition:1st ed. 2019
Series:Springer Monographs in Mathematics
Subjects:
Associative Rings And Algebras
Functional Analysis
Mathematical Logic
Operator Theory
Rings (algebra)
Mathematical Logic And Foundations
Associative Rings
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of Contents:
  • 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

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