Forcing For Mathematicians, 1st Edition

  • Published By: World Scientific Publishing Company
  • ISBN-10: 9814566012
  • ISBN-13: 9789814566018
  • DDC: 511.3
  • Grade Level Range: College Freshman - College Senior
  • 152 Pages | eBook
  • Original Copyright 2014 | Published/Released December 2014
  • This publication's content originally published in print form: 2014

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Ever since Paul Cohens 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.

Table of Contents

Front Cover.
Half Title Page.
Title Page.
Copyright Page.
1: Peano Arithmetic.
2: Zermelo-Fraenkel Set Theory.
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 βℕ \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 βℕ \ 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.
Notation Index.
Subject Index.