Zermelo's Axiom of Choice: Its Origins, Development, and Influence
Courier Corporation, 20 de set. 2012 - 410 pàgines
The Axiom of Choice is the most controversial axiom in the entire history of mathematics. Yet it remains a crucial assumption not only in set theory but equally in modern algebra, analysis, mathematical logic, and topology (often under the name Zorn's Lemma). This treatment is the only full-length history of the axiom in English, and is much more complete than the two other books on the subject, one in French and the other in Russian. This book covers the Axiom's prehistory of implicit uses in the 19th century, its explicit formulation by Zermelo in 1904, the firestorm of controversy that it caused — in England, France, Germany, Italy, and the U.S. — its role in stimulating his axiomatization of set theory in 1908, and its proliferating uses all over mathematics throughout the 20th century.
The book is written so as to be accessible to the advanced mathematics undergraduate, but equally to be informative and stimulating to the professional mathematician. Most technical terms are defined in footnotes, making it accessible by students of the philosophy of mathematics as well.
This new edition has an expanded bibliography and a new preface examining developments since its original 1982 publication.
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Zermelo’s Axiom of Choice: Its Origins, Development, and Influence
Previsualització limitada - 2012
Zermelo's axiom of choice: its origins, development, and influence
Gregory H. Moore
Visualització de fragments - 1982
aleph algebra arbitrary choices argument Assumption Axiom of Choice Axiom of Constructibility Axiom of Separation axiomatic set theory axiomatization Baire Bernstein Boolean Prime Ideal Borel Burali-Forti’s Cantor cardinal number consistency Continuum Hypothesis Countable Union Theorem Dedekind Dedekind-ﬁnite deduced deﬁnable deﬁned demonstrated denumerable Denumerable Axiom Dependent Choices disjoint domain element equipollent equivalent established existence ﬁeld ﬁnite set ﬁrst ﬁrst-order logic Fraenkel function f Godel Hadamard Hausdorff Hilbert independence inﬁnite cardinal inﬁnite set inﬁnitely many arbitrary inﬂuenced Jourdain Konig Kuratowski later Lebesgue Lebesgue’s Levi limit point mathematicians mathematics maximal principles model of ZF Mostowski Multiplicative Axiom non-measurable set notion obtained ordinal paradox Partition Principle Peano postulate Prime Ideal Theorem proposition proved real functions real numbers result Russell Russell’s satisﬁed Schoenﬂies second number-class sequence set theory Sierpinski signiﬁcant Skolem Tarski topological space topology transﬁnite Trichotomy Trichotomy of Cardinals uncountable Well-Ordering Principle Well-Ordering Theorem Zermelo’s Axiom Zermelo’s proof Zermelo’s system