Book:Paul Bernays/Axiomatic Set Theory/Second Edition

Subject Matter

 * Axiomatic Set Theory

Contents



 * PART $\text {I}$. HISTORICAL INTRODUCTION by :


 * $1$.
 * $2$.
 * $3$.
 * $4$.
 * $5$.
 * $6$.
 * $7$.


 * PART $\text {II}$. AXIOMATIC SET THEORY




 * 1. Predicate Calculus; Class Terms and Descriptions; Explicit Definitions
 * 2. Equality and Extensionality. Application to Descriptions
 * 3. Class Formalism. Class Operations
 * 4. Functionality and Mappings
 * 4. Functionality and Mappings


 * 1. The Axioms of General Set Theory
 * 2. Aussonderungstheorem. Intersection
 * 3. Sum Theorem. Theorem of Replacement
 * 4. Functional Sets. One-to-one Correspondences
 * 4. Functional Sets. One-to-one Correspondences


 * 1. Fundaments of the Theory of Ordinals
 * 2. Existential Statements on Ordinals. Limit Numbers
 * 3. Fundamentals of Number Theory
 * 4. Iteration. Primitive Recursion
 * 5. Finite Sets and Classes
 * 5. Finite Sets and Classes


 * 1. The General Recursion Theorem
 * 2. The Schema of Transfinite Recursion
 * 3. Generated Numeration
 * 3. Generated Numeration


 * 1. Comparison of Powers
 * 2. Order and Partial Order
 * 3. Wellorder
 * 3. Wellorder


 * 1. The Potency Axiom
 * 2. The Axiom of Choice
 * 3. The Numeration Theorem. First Concepts of Cardinal Arithmetic
 * 4. Zorn's Lemma and Related Principles
 * 5. Axiom of Infinity. Denumerability
 * 5. Axiom of Infinity. Denumerability


 * 1. Theory of Real Numbers
 * 2. Some Topics of Ordinal Arithmetic
 * 3. Cardinal Operations
 * 4. Formal Laws on Cardinals
 * 5. Abstract Theories
 * 5. Abstract Theories


 * 1. A Strengthening of the Axiom of Choice
 * 2. The Fundierungsaxiom
 * 3. A one-to-one Correspondence between the Class of Ordinals and the Class of all Sets
 * 3. A one-to-one Correspondence between the Class of Ordinals and the Class of all Sets




 * Predicates
 * Functors and Operators
 * Primitive Symbols
 * Primitive Symbols