Book:Paul J. Cohen/Set Theory and the Continuum Hypothesis

Subject Matter

 * Set Theory
 * The Continuum Hypothesis

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