Zermelo’s Axiom of Choice: Its Origins, Development, and Influence

Description

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. A few remarks about format are in order. In this book a publication is indicated by a date after a name; so Hilbert 1926, 178 refers to page 178 of an article written by Hilbert, published in 1926, and listed in the bibliography. Front Matter....Pages i-xiv Prologue....Pages 1-4 The Prehistory of the Axiom of Choice....Pages 5-84 Zermelo and His Critics (1904–1908)....Pages 85-141 Zermelo’s Axiom and Axiomatization in Transition (1908–1918)....Pages 142-195 The Warsaw School, Widening Applications, Models of Set Theory (1918–1940)....Pages 196-292 Epilogue: After Gödel....Pages 293-307 Conclusion....Pages 308-310 Back Matter....Pages 311-411