Book:Paul J. Cohen/Set Theory and the Continuum Hypothesis
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Paul J. Cohen: Set Theory and the Continuum Hypothesis
Published $\text {1966}$, Benjamin
Subject Matter
Contents
- Preface
- Chapter I. General Background in Logic
- 1. Introduction
- 2. Formal Languages
- 3. Universally Valid Statements
- 4. Gödel Completeness Theorem
- 5. The Löwenheim-Skolem Theorem
- 6. Examples of Formal Systems
- 7. Primitive Recursive Functions
- 8. General Recursive Functions
- 9. Gödel Incompleteness Theorem
- 10. Generalized Incompleteness Theorem
- 11. Further Results in Recursive Functions
- Chapter II. Zermelo-Fraenkel Set Theory
- 1. Axioms
- 2. Discussion of the Axioms
- 3. Ordinal Numbers
- 4. Cardinal Numbers
- 5. The Axiom of Regularity
- 6. The System of Gödel-Bernays
- 7. Higher Axioms and Models for Set Theory
- 8. Löwenheim-Skolem Theorem Revisited
- Chapter III. The Consistency of the Continuum Hypothesis and the Axiom of Choice
- 1. Introduction
- 2. Proof of Theorem 1
- 3. Absoluteness
- 4. Proof of AC and GCH in L
- 5. Relations with GB
- 6. The Minimal Model
- Chapter IV. The Independence of the Continuum Hypothesis and the Axiom of Choice
- 1. Introduction
- 2. Intuitive Motivation
- 3. The Forcing Concept
- 4. The Main Lemmas
- 5. The Definability of Forcing
- 6. The Model N
- 7. The General Forcing Concept
- 8. The Continuum Hypothesis
- 9. The Axiom of Choice
- 10. Changing Cardinalities
- 11. Avoiding SM
- 12. GCH Implies AC
- 13. Conclusion
- References