PREFACE TO THE REVISED EDITION -- PREFACE TO THE FIRST EDITION -- CONTENTS -- INTRODUCTION -- Part One. The Elements -- I. LOGIC -- 1. Quantification and identity -- 2. Virtual classes -- 3. Virtual relations -- II. REAL CLASSES -- 4. Reality, extensionality, and the individual -- 5. The virtual amid the real -- 6. Identity and substitution -- III. CLASSES OF CLASSES -- 7. Unit classes -- 8. Unions, intersections, descriptions -- 9. Relations as classes of pairs -- 10. Functions -- IV. NATURAL NUMBERS -- 11. Numbers unconstrued -- 12. Numbers construed -- 13. Induction -- V. ITERATION AND ARITHMETIC -- 14. Sequences and iterates -- 15. The ancestral -- 16. Sum, product, power -- Part Two. Higher Forms of Number -- VI. REAL NUMBERS -- 17. Program. Numerical pairs -- 18. Ratios and reaIs construed -- 19. Existential needs. Operations and extensions -- VII. ORDER AND ORDINALS -- 20. Transfinite induction -- 21. Order -- 22. Ordinal numbers -- 23. Laws of ordinals -- 24. The order of the ordinals -- VIII. TRANSFINITE RECURSION -- 25. Transfinite recursion -- 26. Laws of transfinite recursion -- 27. Enumeration -- IX. CARDINAL NUMBERS -- 28. Comparative size of classes -- 29. The Schröder-Bernstein theorem -- 30. Infinite cardinal numbers -- X. THE AXIOM OF CHOICE -- 31. Selections and selectors -- 32. Further equivalents of the axiom -- 33. The place of the axiom -- Part Three. Axiom Systems -- XI. RUSSELL'S THEORY OF TYPES -- 34. The constructive part -- 35. Classes and the axiom of reducibility -- 36. The modern theory of types -- XII. GENERAL VARIABLES AND ZERMELO -- 37. The theory of types with general variables -- 38. Cumulative types and Zermelo -- 39. Axioms of infinity and others -- XIII. STRATIFICATION AND ULTIMATE CLASSES -- 40. "New foundations" -- 41. Non-Cantorian classes. Induction again -- 42. Ultimate classes added.

XIV. VON NEUMANN'S SYSTEM AND OTHERS -- 43. The von Neumann-Bernays system -- 44. Departures and comparisons -- 45. Strength of systems -- SYNOPSIS OF FIVE AXIOM SYSTEMS -- LIST OF NUMBERED FORMULAS -- BIBLIOGRAPHICAL REFERENCES -- INDEX.