Book:Winfried Just/Discovering Modern Set Theory. I: The Basics
Jump to navigation
Jump to search
Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics
Published $\text {1996}$, American Mathematical Society
- ISBN 0-8218-0266-6
Subject Matter
Contents
- Preface
- How to Read this Book
- Basic Notations
- Introduction
- Part $1$. Not Entirely Naive Set Theory
- Chapter $1$. Pairs, Relations, and Functions
- Chapter $2$. Partial Order Relations
- Chapter $3$. Cardinality
- Chapter $4$. Induction
- $4.1$ Induction and recursion over the set of natural numbers
- $4.2$ Induction and recursion over wellfounded sets
- Part $2$. An Axiomatic Foundation of Set Theory
- Chapter $5$. Formal Languages and Models
- Chapter $6$. Power and Limitations of the Axiomatic Method
- $6.1$ Complete theories
- $6.2$ The Incompleteness Phenomenon
- $6.3$ Definability
- Chapter $7$. The Axioms
- Chapter $8$. Classes
- Chapter $9$. Versions of the Axiom of Choice
- $9.1$ Statements Equivalent to the Axiom of Choice
- $9.2$ Set Theory without the Axiom of Choice
- $9.3$ The Axiom of Determinacy
- $9.4$ The Banach-Tarski Paradox
- Chapter $10$. The Ordinals
- $10.1$ The Class $\mathbf {ON}$
- $10.2$ Ordinal Arithmetic
- Chapter $11$. The Cardinals
- $11.1$ Initial Ordinals
- $11.2$ Cardinal Arithmetic
- Chapter $12$. Pictures of the Universe
- Subject index
- Index of notation
Source work progress
- 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics ... (previous) ... (next): Part $1$: Not Entirely Naive Set Theory: Chapter $3$: Cardinality: Exercise $3$
- A complexity raised here which needs to be resolved:
- 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics ... (previous) ... (next): Part $1$: Not Entirely Naive Set Theory: Chapter $1$: Pairs, Relations, and Functions: Exercise $8$