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Introduction

The Elements / Part 1：

Logic Quantification and identity Virtual Classes Virtual relations / I：

Real Classes Reality, extensionality, and The individual The virtual Amid The real Identity and substitution / II：

Classes of Classes Unit Classes Unions, intersections, descriptions Relations As Classes of pairs Functions / III：

Natural Numbers Numbers unconstrued Numbers construed Induction / IV：

Iteration and Arithmetic Sequences and iterates The Ancestral Sum, product, power / V：

Higher Forms of Number / Part 2：

Real Numbers Program. / VI：

Numerical pairs Ratios and reals construed Existential needs.

Operations and extensions

Order and Ordinals Transfinite induction / VII：

Order Ordinal numbers Laws of ordinals

The order of The ordinals

Transfinite Recursion / VIII：

Transfinite recursion Laws of Transfinite recursion Enumeration

Cardinal Numbers Comparative size of Classes / IX：

The SchrOder-Bernstein

Theorem Infinite cardinal numbers

The Axiom of Choice Selections and selectors / X：

Further equivalents of The Axiom

The place of The Axiom

Axiom Systems / Part 3：

Russell'S Theory of Types / XI：

The constructive part Classes and The Axiom of reducibility

The modern Theory of types

General Variables and Zermelo / XII：

The Theory of types with general variables

Cumulative types and Zermelo Axioms of infinity and Others

Stratification and Ultimate Classes "New foundations" Non-Cantorian Classes. / XIII：

Induction Again Ultimate Classes Added

Von Neumann'S System and Others / XIV：

The von Neumann-Bernays system Departures and comparisons Strength of systems

Synopsis of Five Axiom Systems List of Numbered Formulas

Bibliographical

References

Index

Introduction

The Elements / Part 1：

Logic Quantification and identity Virtual Classes Virtual relations / I：