Hausdorff on Ordered Sets
American Mathematical Soc. - 322 pàgines
Georg Cantor, the founder of set theory, published his last paper on sets in 1897. In 1900, David Hilbert made Cantor's Continuum Problem and the challenge of well-ordering the real numbers the first problem of his famous lecture at the international congress in Paris. Thus, as the nineteenth century came to a close and the twentieth century began, Cantor's work was finally receiving its due and Hilbert had made one of Cantor's most important conjectures his number one problem. It was time for the second generation of Cantorians to emerge. Foremost among this group were Ernst Zermelo and Felix Hausdorff. Zermelo isolated the Choice Principle, proved that every set could be well-ordered, and axiomatized the concept of set. He became the father of abstract set theory. Hausdorff eschewed foundations and developed set theory as a branch of mathematics worthy of study in its own right, capable of supporting both general topology and measure theory. He is recognized as the era's leading Cantorian. Hausdorff published seven articles in set theory during the period 1901-1909, mostly about ordered sets. This volume contains translations of these papers with accompanying introductory essays. They are highly accessible, historically significant works, important not only for set theory, but also for model theory, analysis and algebra. This book is suitable for graduate students and researchers interested in set theory and the history of mathematics. Also available from the AMS by Felix Hausdorff are the classic work, Grundzuge der Mengenlehre, and its English translation, Set Theory, as Volume 69 and Volume 119 in the AMS Chelsea Publishing series. Information for our distributors: Copublished with the London Mathematical Society. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.
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About a Certain Kind of Ordered Sets H 1901b ll
Investigations into Order Types H 1906b
Introduction to Investigations into Order Types IV V
Investigations into Order Types H 1907a
Introduction to About Dense Order Types
The Fundamentals of a Theory of Ordered Sets H 1908
Introduction to Graduation by Final Behavior
Appendix Sums of N Sets H 1936b
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according addition already appears arbitrary argument base belong Bernstein boundary called Cantor's cardinality certainly character cofinal coinitial combinations complete consider construction contains continuous continuum convergent corresponding countable course coverings defined definition denote determined differences distinct divergent equal everywhere dense example exists final finite follows functions fundamental further gaps given going graded set Hausdorff hence holds homogeneous types immediately infinitary initial segment interval kind last element least limit middle segment namely number class numerical sequences obtain occur order types ordered domain ordered set ordinal number pair pantachie particular piece positive possible powers principal principal element problem proof properties proved question rank ordering rational regular initial number relation remaining represented respect result ring roots runs set theory similar species subset Theorem u;-sequence unbounded