Zermelo's Axiom of Choice: Its Origins, Developments, and Influence
by Gregory H. Moore

Prologue

Chapter 1: The Prehistory of the Axiom of Choice

Chapter 2: Zermelo and His Critics (1904-1908)

Chapter 3: Zermelo's Axiom and Axiomatization in Transition (1908-1918)

Chapter 4: The Warsaw School, Widening Applications, Models of Set Theory (1918-1940)

Epilogue: After Goedel

Conclusion

Appendix I: Five Letters on Set Theory

Appendix II: Deductive Relations Concerning the Axiom of Choice

From the Preface:

This book grew out of my interest in what is common to three disciplines: mathematics, philosophy, and history. The origins of Zermelo's Axiom of Choice, as well as the controversy that it engendered, certainly lie in that intersection. Since the time of Aristotle, mathematics has been concerned alternately with its assumptions and with the objects, such as number and space, about which those assumptions were made. In the historical context of Zermelo's Axiom, I have explored both the vagaries and the fertility of this alternating concern. Though Zermelo's research has provided the focus for this book, much of it is devoted to the problems from which his work originated and to the later developments which, directly or indirectly, he inspired.

See also