INTRODUCTION
PART ONE. THE ELEMENTS
I. LOGIC
Quantification and identity
Virtual classes
Virtual relations
II. REAL CLASSES
Reality, extensionality, and the individual
The virtual amid the real
Identity and substitution
III. CLASSES OF CLASSES
Unit classes
Unions, intersections, descriptions
Relations as classes of pairs
Functions
IV. NATURAL NUMBERS
Numbers unconstrued
Numbers construed
Induction
V. ITERATION AND ARITHMETIC
Sequences and iterates
The ancestral
Sum, product, power
PART TWO. HIGHER FORMS OF NUMBER
VI. REAL NUMBERS
Program. Numerical pairs
Ratios and reals construed
Existential needs. Operations and extensions
VII. ORDER AND ORDINALS
Transfinite induction
Order
Ordinal numbers
Laws of ordinals
The order of the ordinals
VIII. TRANSFINITE RECURSION
Transfinite recursion
Laws of transfinite recursion
Enumeration
IX. CARDINAL NUMBERS
Comparative size of classes
The SchrOder-Bernstein theorem
Infinite cardinal numbers
X. THE AXIOM OF CHOICE
Selections and selectors
Further equivalents of the axiom
The place of the axiom
PART THREE. AXIOM SYSTEMS
XI. RUSSELL'S THEORY OF TYPES
The constructive part
Classes and the axiom of reducibility
The modern theory of types
XII. GENERAL VARIABLES AND ZERMELO
The theory of types with general variables
Cumulative types and Zermelo
Axioms of infinity and others
XIII. STRATIFICATION AND ULTIMATE CLASSES
"New foundations"
Non-Cantorian classes. Induction again
Ultimate classes added
XIV. VON NEUMANN'S SYSTEM AND OTHERS
The von Neumann-Bernays system
Departures and comparisons
Strength of systems
SYNOPSIS OF FIVE AXIOM SYSTEMS
LIST OF NUMBERED FORMULAS
BIBLIOGRAPHICAL REFERENCES
INDEX