Details

Autor(en) / Beteiligte

• Rosser, J. Barkley

Titel

Simplified independence proofs : Boolean valued models of set theory

Beschreibungen/Notizen

• Description based upon print version of record.
• Includes bibliography.
• 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 VD. 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 CaseA. 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 TheoremChapter 10. Resolution of Conceptual Difficulties; A. What Is Truth?; B. Appeal to Strong Axioms; Bibliography; Subject Index
• Simplified independence proofs
• English