Book:Winfried Just/Discovering Modern Set Theory. I: The Basics

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

• Set Theory

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

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