Proofs of the CantorBernstein theorem [electronic resource] : a mathematical excursion
 Responsibility
 Arie Hinkis.
 Imprint
 Heidelberg ; New York : Birkhäuser, c2013.
 Physical description
 1 online resource (426 p.)
 Series
 Science networks historical studies.
Online
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Description
Creators/Contributors
 Author/Creator
 Hinkis, Arie.
Contents/Summary
 Bibliography
 Includes bibliographical references and indexes.
 Contents

 Preface.  Part I: Cantor and Dedekind. Cantor's CBT proof for sets of the power of (II). Generalizing Cantor's CBT proof. CBT in Cantor's 1878 Beitrag. The theory of inconsistent sets. Comparability in Cantor's writings. The scheme of complete disjunction. Ruptures in the CantorDedekind correspondence. The inconsistency of Dedekind's infinite set. Dedekind's proof of CBT. Part II: The early proofs. Schroeder's Proof of CBT. Bernstein, Borel and CBT. Schoenflies' 1900 proof of CBT. Zermelo's 1901 proof of CBT. Bernstein's Division Theorem. Part III: Under the logicist sky. Russell's 1902 proof of CBT. The role of CBT in Russell's Paradox. Jourdain's 1904 generalization of Grundlagen. Harward 1905 on Jourdain 1904. Poincare and CBT. Peano's proof of CBT. J. Konig's strings gestalt. From kings to graphs. Jourdain's improvements round. Zermelo's 1908 proof of CBT. Korselt's proof of CB. Proofs of CBT in Principia Mathematica. The origin of Hausdorff Paradox in BDT. Part IV: At the Polish school. Sierpinski's proofs of BDT. Banach's proof of CBT. Kuratowski's proof of BDT. Early fixedpoint CBT proofs: Whittaker
 TarskiKnaster. CBT and BDT for ordertypes. Sikorski's proof of CBT for Boolean algebras. Tarski's proofs of BDT and the inequalityBDT. Tarski's FixedPoint Theorem and CBT. Reichbach's proof of CBT. Part V: Other ends and beginnings. Hellmann's proof of CBT. CBT and intuitionism. CBT in category theory. Conclusion. Bibliography. Index of names. Index of subjects.
 (source: Nielsen Book Data)
 Publisher's summary

This book offers an excursion through the developmental area of research mathematics. It presents some 40 papers, published between the 1870s and the 1970s, on proofs of the CantorBernstein theorem and the related Bernstein division theorem. While the emphasis is placed on providing accurate proofs, similar to the originals, the discussion is broadened to include aspects that pertain to the methodology of the development of mathematics and to the philosophy of mathematics. Works of prominent mathematicians and logicians are reviewed, including Cantor, Dedekind, Schroeder, Bernstein, Borel, Zermelo, Poincare, Russell, Peano, the Koenigs, Hausdorff, Sierpinski, Tarski, Banach, Brouwer and several others mainly of the Polish and the Dutch schools. In its attempt to present a diachronic narrative of one mathematical topic, the book resembles Lakatos' celebrated book Proofs and Refutations. Indeed, some of the observations made by Lakatos are corroborated herein. The analogy between the two books is clearly anything but superficial, as the present book also offers new theoretical insights into the methodology of the development of mathematics (proofprocessing), with implications for the historiography of mathematics.
(source: Nielsen Book Data)
Subjects
 Subjects
 Set theory.
Bibliographic information
 Publication date
 2013
 Series
 Science Networks. Historical Studies ; v. 45
 ISBN
 9783034802246 (electronic bk.)
 3034802242 (electronic bk.)
 9783034802239