Читать книгу Set Theory And Foundations Of Mathematics: An Introduction To Mathematical Logic - Volume I: Set Theory - Douglas Cenzer - Страница 7

Preface

About the Authors

1. Introduction

2. Review of Sets and Logic

2.1 The Algebra of Sets

2.2 Relations

2.3 Functions

2.4 Equivalence Relations

2.5 Orderings

2.6 Trees

3. Zermelo–Fraenkel Set Theory

3.1 Historical Context

3.2 The Language of the Theory

3.3 The Basic Axioms

3.4 Axiom of Infinity

3.5 Axiom Schema of Comprehension

3.6 Axiom of Choice

3.7 Axiom Schema of Replacement

3.8 Axiom of Regularity

4. Natural Numbers and Countable Sets

4.1 Von Neumann’s Natural Numbers

4.2 Finite and Infinite Sets

4.3 Inductive and Recursive Definability

4.4 Cardinality

4.5 Countable and Uncountable Sets

5. Ordinal Numbers and the Transfinite

5.1 Ordinals

5.2 Transfinite Induction and Recursion

5.3 Ordinal Arithmetic

5.4 Ordinals and Well-Orderings

6. Cardinality and the Axiom of Choice

6.1 Equivalent Versions of the Axiom of Choice

6.2 Applications of the Axiom of Choice

6.3 Cardinal Numbers

7. Real Numbers

7.1 Integers and Rational Numbers

7.2 Dense Linear Orders

7.3 Complete Orders

7.4 Countable and Uncountable Sets of Reals

7.5 Topological Spaces

8. Models of Set Theory

8.1 The Hereditarily Finite Sets

8.2 Transfinite Models

9. Ramsey Theory

9.1 Finite Patterns

9.2 Countably Infinite Patterns

9.3 Uncountable Patterns

Bibliography

Index