Hausdorff On Ordered Sets

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Hausdorff On Ordered Sets

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Author : Felix Hausdorff
language : en
Publisher:
Release Date : 2005

Hausdorff On Ordered Sets written by Felix Hausdorff and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Functions categories.

Hausdorff On Ordered Sets

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Author : Felix Hausdorff
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Hausdorff On Ordered Sets written by Felix Hausdorff and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

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 in his famous Paris lecture. It was time for the appearance of the second generation of Cantorians. They emerged in the decade 1900-1909, and foremost among them 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 pursued set theory as part of the mathematical arsenal. He was recognized as the era's leading Cantorian. From 1901-1909, Hausdorff published seven articles in which he created a representation theory for ordered sets and investigated sets of real sequences partially ordered by eventual dominance, together with their maximally ordered subsets. These papers are translated and appear in this volume. Each is accompanied by an introductory essay. These highly accessible works are of historical significance, not only for set theory, but also for model theory, analysis and algebra.

Hausdorff On Ordered Sets

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Author : Felix Hausdorff
language : en
Publisher: American Mathematical Soc.
Release Date :

Hausdorff On Ordered Sets written by Felix Hausdorff and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

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.

Non Hausdorff Topology And Domain Theory

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Author : Jean Goubault-Larrecq
language : en
Publisher: Cambridge University Press
Release Date : 2013-03-28

Non Hausdorff Topology And Domain Theory written by Jean Goubault-Larrecq and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-28 with Computers categories.

Introduces the basic concepts of topology with an emphasis on non-Hausdorff topology, which is crucial for theoretical computer science.

Set Theory

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Author : Felix Hausdorff
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-08-24

Set Theory written by Felix Hausdorff and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-24 with Education categories.

This work is a translation into English of the Third Edition of the classic German language work Mengenlehre by Felix Hausdorff published in 1937. From the Preface (1937): “The present book has as its purpose an exposition of the most important theorems of the theory of sets, along with complete proofs, so that the reader should not find it necessary to go outside this book for supplementary details while, on the other hand, the book should enable him to undertake a more detailed study of the voluminous literature on the subject. The book does not presuppose any mathematical knowledge beyond the differential and integral calculus, but it does require a certain maturity in abstract reasoning; qualified college seniors and first year graduate students should have no difficulty in making the material their own … The mathematician will … find in this book some things that will be new to him, at least as regards formal presentation and, in particular, as regards the strengthening of theorems, the simplification of proofs, and the removal of unnecessary hypotheses.”

Ordered Sets

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Author : Egbert Harzheim
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-07-25

Ordered Sets written by Egbert Harzheim and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-07-25 with Mathematics categories.

This book is written particularly for mathematics students and, of course, for mathematicians interested in set theory. Only some fun- mental parts of naive set theory are presupposed, - not more than is treated in a textbook on set theory, even if this restricts us only to the most basic facts of this field. We have summarized all of this in Chapter 0 without longer discusssions and explanations, because there are s- eral textbooks which can be consulted by the reader, e.g. HrbacekIJech [88], KneeboneIRotman [99], ShenIVereshchagin [159]. Besides this only elementary facts of analysis are used. The theory of ordered sets can be divided into two parts, depending on whether the sets under consideration are finite or infinite. The first part is grounded mainly in combinatorics and graph theory and does not make essential use of set-theorical concepts, whereas the second part presupposes a knowledge of the fundamental notions of set theory, in particular of the system of ordinal and cardinal numbers. In this book we mainly deal with general infinite ordered sets. In this field the textbook literature is still very small. Therefore this book supplements the existing literature.

Logical Methods

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Author : John N. Crossley
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-01-26

Logical Methods written by John N. Crossley and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-26 with Computers categories.

The twenty-six papers in this volume reflect the wide and still expanding range of Anil Nerode's work. A conference on Logical Methods was held in honor of Nerode's sixtieth birthday (4 June 1992) at the Mathematical Sciences Institute, Cornell University, 1-3 June 1992. Some of the conference papers are here, but others are from students, co-workers and other colleagues. The intention of the conference was to look forward, and to see the directions currently being pursued, in the development of work by, or with, Nerode. Here is a brief summary of the contents of this book. We give a retrospective view of Nerode's work. A number of specific areas are readily discerned: recursive equivalence types, recursive algebra and model theory, the theory of Turing degrees and r.e. sets, polynomial-time computability and computer science. Nerode began with automata theory and has also taken a keen interest in the history of mathematics. All these areas are represented. The one area missing is Nerode's applied mathematical work relating to the environment. Kozen's paper builds on Nerode's early work on automata. Recursive equivalence types are covered by Dekker and Barback, the latter using directly a fundamental metatheorem of Nerode. Recursive algebra is treated by Ge & Richards (group representations). Recursive model theory is the subject of papers by Hird, Moses, and Khoussainov & Dadajanov, while a combinatorial problem in recursive model theory is discussed in Cherlin & Martin's paper. Cenzer presents a paper on recursive dynamics.

Paradoxes Of Measures And Dimensions Originating In Felix Hausdorff S Ideas

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Author : Janusz Czyz
language : en
Publisher: World Scientific
Release Date : 1994-01-14

Paradoxes Of Measures And Dimensions Originating In Felix Hausdorff S Ideas written by Janusz Czyz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-14 with Mathematics categories.

In this book, many ideas by Felix Hausdorff are described and contemporary mathematical theories stemming from them are sketched.

Sets And Extensions In The Twentieth Century

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Author :
language : en
Publisher: Elsevier
Release Date : 2012-01-24

Sets And Extensions In The Twentieth Century written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-24 with Mathematics categories.

Set theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mathematics that both proceeds with its own internal questions and is capable of contextualizing over a broad range, which makes set theory an intriguing and highly distinctive subject. This handbook covers the rich history of scientific turning points in set theory, providing fresh insights and points of view. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in mathematics, the history of philosophy, and any discipline such as computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration - Serves as a singular contribution to the intellectual history of the 20th century - Contains the latest scholarly discoveries and interpretative insights

A Delicate Balance Global Perspectives On Innovation And Tradition In The History Of Mathematics

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Author : David E. Rowe
language : en
Publisher: Birkhäuser
Release Date : 2015-05-12

A Delicate Balance Global Perspectives On Innovation And Tradition In The History Of Mathematics written by David E. Rowe and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-12 with Mathematics categories.

Joseph W. Dauben, a leading authority on the history of mathematics in Europe, China, and North America, has played a pivotal role in promoting international scholarship over the last forty years. This Festschrift volume, showcasing recent historical research by leading experts on three continents, offers a global perspective on important themes in this field.