A Set Theory Workbook

1. Front Matter

   Pages i-viii

   PDF

2. Introduction

   1. Introduction

      • Iain T. Adamson

      Pages 3-4

3. Exercises

   1. Front Matter

      Pages 5-5

      PDF

   2. First Axioms of the Theory NBG

      • Iain T. Adamson

      Pages 7-11

   3. Relations

      • Iain T. Adamson

      Pages 13-17

   4. Functional Relations and Mappings

      • Iain T. Adamson

      Pages 19-27

   5. Families of Sets

      • Iain T. Adamson

      Pages 29-34

   6. Equivalence Relations

      • Iain T. Adamson

      Pages 35-39

   7. Order Relations

      • Iain T. Adamson

      Pages 41-45

   8. Well-Ordering

      • Iain T. Adamson

      Pages 47-50

   9. Ordinals

      • Iain T. Adamson

      Pages 51-54

   10. Natural Numbers

       • Iain T. Adamson

       Pages 55-57

   11. Equivalents of the Axiom of Choice

       • Iain T. Adamson

       Pages 59-62

   12. Infinite Sets

       • Iain T. Adamson

       Pages 63-64

   13. Cardinals

       • Iain T. Adamson

       Pages 65-67

   14. Cardinal and Ordinal Arithmetic

       • Iain T. Adamson

       Pages 69-73

4. Answers

   1. Front Matter

      Pages 75-75

      PDF

   2. Answers to Chapter 1

      • Iain T. Adamson

      Pages 77-79

   3. Answers to Chapter 2

      • Iain T. Adamson

      Pages 81-84

   4. Answers to Chapter 3

      • Iain T. Adamson

      Pages 85-93

This book is a companion to A general topology workbook published by Birkhiiuser last year. In an ideal world the order of publication would have been reversed, for the notation and some of the results of the present book are used in the topology book and on the other hand (the reader may be assured) no topology is used here. Both books share the word Workbook in their titles. They are based on the principle that for at least some branches of mathematics a good way for a student to learn is to be presented with a clear statement of the definitions of the terms with which the subject is concerned and then to be faced with a collection of problems involving the terms just defined. In adopting this approach with my Dundee students of set theory and general topology I found it best not to differentiate too precisely between simple illustrative examples, easy exercises and results which in conventional textbooks would be labelled as Theorems.

• Arithmetic
• Equivalence
• Finite
• Mathematics
• Set Theory
• axiom of choice
• cardinals
• function
• ksa
• ordinal
• well-ordering principle

"An unconventional approach to the basic course in set theory... The material...can serve as the text for a one-semester course or as a supplement to a larger course... Presents basic definitions and exercises [and] provides solutions to given examples in a very clear style, so anyone can check his own approach and improve his mathematical style. Strongly recommended..."

–EMS Newsletter

• Department of Mathematics, The University of Dundee, Dundee, Scotland

  Iain T. Adamson

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