Set Theory and its Philosophy: A Critical Introduction

Content Headings:

• I. Sets • Introduction to Part I • 1. Logic • 2. Collections • 3. The hierarchy • 4. The theory of sets • Conclusion to Part I

• II. Numbers • Introduction to Part II • 5. Arithmetic • 6. Counting • 7. Lines • 8. Real numbers • Conclusion to Part II

• III. Cardinals and Ordinals • Introduction to Part III • 9. Cardinals • 10. Basic cardinal arithmetic • 11. Ordinals • 12. Ordinal arithmetic • Conclusion to Part III

• IV. Further Axioms • Introduction to Part IV • 13. Orders of infinity • 14. The axiom of choice • 15. Further cardinal arithmetic • Conclusion to Part IV

• Appendices • A. Traditional axiomatizations • B. Classes • C. Sets and classes • References • List of symbols • Index of definitions • Index of names

Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.