Simplified Independence Proofs
Simplified Independence Proofs
Published on 29. August 2011
216 pages
978-0-08-087343-5 (ISBN)
Description
Simplified Independence Proofs
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Content
- Front Cover
- Simplified Independence Proofs: Boolean Valued Models of Set Theory
- Copyright Page
- Contents
- Preface
- Glossary of Symbols
- Location of Theorems
- Locations of Definations
- Chapter 1. General Remarks
- A. Background Materials
- B. Assumptions
- C. Summary of Results
- D. A Paradigm for the Proofs
- E. A Guide for the Casual Reader
- Chapter 2. Boolean Algebra
- A. Topological Spaces
- B. Properties of Boolean Algebras
- C. Automorphisms
- D. The Countable Chain Condition
- Chapter 3. The Basic Model
- A. Axioms of the Restricted Predicate Calculus
- B. Axioms of Equality and Extensionality
- C. Methods for Defining Members of V
- D. The Basic Set Theory Axioms
- E. Ordinals and Cardinals in the Model
- F. The Axiom of Choice
- Chapter 4. The Independence of V = L
- A. Preliminaries
- B. Proof of GCH
- C. Subsets of ?
- Chapter 5. Analogies with Forcing
- A. Comparison of Specific Proofs
- B. Replacing Boolean Algebra by Forcing in Proofs?
- Chapter 6. The Independence of AxC
- A. The Key Idea of the Proof
- B. The Choice of G
- C. Subsets of ?
- D. The Real Numbers Are Not Well-ordered
- Chapter 7. The Independence of the Continuum Hypothesis
- A. The Key Result
- B. Additional Cardinality Results
- Chapter 8. The Generalized GCH-The Bounded Case
- A. Statement of Easton's Theorem
- B. Specification of the Boolean Algebra
- C. Substitutes for the Cohen Combinatorial Lemma
- D. Cardinality Relations
- E. Proof of Easton's Theorem
- F. A Note on the Proof
- Chapter 9. The Generalized GCH-The Unbounded Case
- A. Preliminary Considerations
- B. Specification of the Boolean Algebra
- C. Definition of the Universe
- D. Definition of the Boolean Value of a Statement
- E. Proof of the Axioms of Set Theory, Except the Power Set Axiom
- F. Cardinality Relations
- G. The Axiom of the Power Set
- H. Proof of Easton's Theorem
- Chapter 10. Resolution of Conceptual Difficulties
- A. What Is Truth?
- B. Appeal to Strong Axioms
- Bibliography
- Subject Index
