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

Portada
Springer Science & Business Media, 6 de des. 2012 - 412 pàgines
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.
 

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Continguts

The Boundary between the Finite and the Infinite
22
Chapter 3
34
The wellordering Problem and the Continuum Hypothesis
39
Implicit Uses by Future Critics
64
Retrospect and Prospect
82
Richard Poincaré and Fréchet
104
Julius and Dénes König
119
Logic vs Zermelos Axiom
134
Zermelos Axiom and Axiomatization in Transition 19081918
142
Chapter 4
196
After Gödel
293
Conclusion
308
Appendix 2
321
Journal Abbreviations Used in the Bibliography
335
Index of Numbered Propositions
379
Copyright

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