Forcing for Mathematicians

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Ever since Paul Cohen's spectacular use of the forcing concept to prove the independence of the continuum hypothesis from the standard axioms of set theory, forcing has been seen by the general mathematical community as a subject of great intrinsic interest but one that is technically so forbidding that it is only accessible to specialists. In the past decade, a series of remarkable solutions to long-standing problems in C*-algebra using set-theoretic methods, many achieved by the author and his collaborators, have generated new interest in this subject. This is the first book aimed at explaining forcing to general mathematicians. It simultaneously makes the subject broadly accessible by explaining it in a clear, simple manner, and surveys advanced applications of set theory to mainstream topics. Readership: Graduates and researchers in logic and set theory, general mathematical audience.

Author(s): Nik Weaver
Publisher: World Scientific
Year: 2014

Language: English
Pages: C, x, 142

1. Peano Arithmetic
2. Zermelo-Fraenkel Set Theory
Zermelo-Fraenkel axioms
3. Well-Ordered Sets
4. Ordinals
5. Cardinals
6. Relativization
7. Reflection
8. Forcing Notions
9. Generic Extensions
10. Forcing Equality
11. The Fundamental Theorem
12. Forcing CH
13. Forcing ¬ CH
14. Families of Entire Functions*
15. Self-Homeomorphisms of ßN \ N I*
16. Pure States on B(H)*
17. The Diamond Principle
18. Suslin’s Problem I*
19. Naimark’s Problem*
20. A Stronger Diamond
21. Whitehead’s Problem I*
22. Iterated Forcing
23. Martin’s Axiom
24. Suslin’s Problem II*
25. Whitehead’s Problem II*
26. The Open Coloring Axiom
27. Self-Homeomorphisms of ßN \ N II*
28. Automorphisms of the Calkin Algebra I*
29. Automorphisms of the Calkin Algebra II*
30. The Multiverse Interpretation
Appendix A Forcing with Preorders
Exercises
Notes
Bibliography
Notation Index
Subject Index