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Proofs of the Cantor-Bernstein Theorem (Record no. 15452)

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003 - CONTROL NUMBER IDENTIFIER
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005 - DATE AND TIME OF LATEST TRANSACTION
control field 20140310145531.0
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
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020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9783034802246
978-3-0348-0224-6
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA21-27
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 510.9
Edition number 23
264 #1 -
-- Basel :
-- Springer Basel :
-- Imprint: Birkhäuser,
-- 2013.
912 ## -
-- ZDB-2-SHU
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Hinkis, Arie.
Relator term author.
245 10 - IMMEDIATE SOURCE OF ACQUISITION NOTE
Title Proofs of the Cantor-Bernstein Theorem
Medium [electronic resource] :
Remainder of title A Mathematical Excursion /
Statement of responsibility, etc by Arie Hinkis.
300 ## - PHYSICAL DESCRIPTION
Extent XXIII, 429 p. 29 illus., 3 illus. in color.
Other physical details online resource.
440 1# - SERIES STATEMENT/ADDED ENTRY--TITLE
Title Science Networks. Historical Studies ;
Volume number/sequential designation 45
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note 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 Cantor-Dedekind correspondence -- The inconsistency of Dedekind's infinite set -- Dedekind's proof of CBT -- Part II: The early proofs -- Schröder'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 -- Poincaré and CBT -- Peano's proof of CBT -- J. Kőnig'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 -- Sierpiński's proofs of BDT -- Banach's proof of CBT -- Kuratowski's proof of BDT -- Early fixed-point CBT proofs: Whittaker; Tarski-Knaster -- CBT and BDT for order-types -- Sikorski's proof of CBT for Boolean algebras -- Tarski's proofs of BDT and the inequality-BDT -- Tarski's Fixed-Point 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.
520 ## - SUMMARY, ETC.
Summary, etc 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 Cantor-Bernstein 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, Schröder, Bernstein, Borel, Zermelo, Poincaré, Russell, Peano, the Königs, 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 (proof-processing), with implications for the historiography of mathematics.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Mathematics.
Topical term or geographic name as entry element Algebra.
Topical term or geographic name as entry element Logic, Symbolic and mathematical.
Topical term or geographic name as entry element Mathematics.
Topical term or geographic name as entry element History of Mathematical Sciences.
Topical term or geographic name as entry element Mathematical Logic and Foundations.
Topical term or geographic name as entry element Category Theory, Homological Algebra.
710 2# - ADDED ENTRY--CORPORATE NAME
Corporate name or jurisdiction name as entry element SpringerLink (Online service)
773 0# - HOST ITEM ENTRY
Title Springer eBooks
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Display text Printed edition:
International Standard Book Number 9783034802239
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier http://dx.doi.org/10.1007/978-3-0348-0224-6
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Source of classification or shelving scheme
Item type E-Book
Copies
Price effective from Permanent location Date last seen Not for loan Date acquired Source of classification or shelving scheme Koha item type Damaged status Lost status Withdrawn status Current location Full call number
2014-04-02AUM Main Library2014-04-02 2014-04-02 E-Book   AUM Main Library510.9
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