Zermelo’s Axiom of Choice: Its Origins, Development, and InfluenceSpringer New York, 17 de nov. 1982 - 410 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. |
Continguts
Chapter 3 | 34 |
Chapter 2 | 48 |
Zermelo and His Critics 19041908 | 85 |
Copyright | |
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Zermelo's Axiom of Choice: Its Origins, Development, and Influence Gregory H. Moore Previsualització limitada - 2012 |
Zermelo’s Axiom of Choice: Its Origins, Development, and Influence G.H. Moore Previsualització limitada - 2012 |
Zermelo’s Axiom of Choice: Its Origins, Development, and Influence G.H. Moore Previsualització no disponible - 2011 |
Frases i termes més freqüents
aleph algebra arbitrary choices argument Assumption Axiom of Choice Axiom of Separation axiomatic set theory axiomatization Baire Bernstein Boolean Prime Ideal Borel Cantor cardinal number consistency Continuum Hypothesis Countable Union Theorem Dedekind Dedekind-finite deduced defined demonstrated denumerable Denumerable Axiom disjoint domain element equipollent equivalent established existence finite number finite set first-order logic Fraenkel function f Gödel Hadamard Hausdorff Hilbert independence infinite cardinal infinite set infinity Jourdain König Kuratowski later Lebesgue Lemma Levi limit point mathematicians mathematics maximal principles measure model of ZF Mostowski Multiplicative Axiom Neumann non-measurable set notion obtained ordinal Partition Principle Peano Poincaré postulate Prime Ideal Prime Ideal Theorem proposition proved real functions real numbers result Russell Russell's Schoenflies second number-class sequence sequential set theory set-theoretic Sierpiński Skolem Steinitz Tarski topological transfinite Trichotomy Trichotomy of Cardinals uncountable urelements well-ordered set Well-Ordering Principle Well-Ordering Theorem Zermelo's Axiom Zermelo's proof Zermelo's system