Hausdorff on ordered sets
Author(s)
Bibliographic Information
Hausdorff on ordered sets
（History of mathematics, v. 25 ; sources）
American Mathematical Society, c2005
- : pbk
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Note
Translated and edited from German
"London Mathematical Society."
"From 1901-1909, Hausdorff published seven articles ... These papers are translated and appear in this volume."--P. [4] of cover
"Selected Hausdorff bibliography": p. 1
Includes bibliographical references (p. 317-322)
Description and Table of Contents
Description
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 works, Grundzuge der Mengenlehre (Volume 61) and Set Theory (Volume 119), in the AMS Chelsea Publishing series.
Table of Contents
Selected Hausdorff bibliography by J. M. Plotkin Introduction to ""About a certain kind of ordered sets"" by J. M. Plotkin About a certain kind of ordered sets [H 1901b] by F. Hausdorff Introduction to ""The concept of power in set theory"" by J. M. Plotkin The concept of power in set theory [H 1904a] by F. Hausdorff Introduction to ""Investigations into order types, I, II, III"" by J. M. Plotkin Investigations into order types [H 1906b] by F. Hausdorff Introduction to ""Investigations into order types IV, V"" by J. M. Plotkin Investigations into order types [H 1907a] by F. Hausdorff Introduction to ""About dense order types"" by J. M. Plotkin About dense order types [H 1907b] by F. Hausdorff Introduction to ""The fundamentals of a theory of ordered sets"" by J. M. Plotkin The fundamentals of a theory of ordered sets [H 1908] by F. Hausdorff Introduction to ""Graduation by final behavior"" by J. M. Plotkin Graduation by final behavior [H 1909a] by F. Hausdorff Appendix. Sums of $\aleph_1$ sets [H 1936b] by F. Hausdorff.
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