Welcome to Central Library, SUST

Proofs of the Cantor-Bernstein Theorem (Record no. 45207)

MARC details
000 -LEADER
fixed length control field 04562nam a22005057a 4500
001 - CONTROL NUMBER
control field sulb-eb0023115
003 - CONTROL NUMBER IDENTIFIER
control field BD-SySUS
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20160413122335.0
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr nn 008mamaa
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 130228s2013 sz | s |||| 0|eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9783034802246
-- 978-3-0348-0224-6
024 7# - OTHER STANDARD IDENTIFIER
Standard number or code 10.1007/978-3-0348-0224-6
Source of number or code doi
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA21-27
072 #7 - SUBJECT CATEGORY CODE
Subject category code PBX
Source bicssc
Subject category code MAT015000
Source bisacsh
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 510.9
Edition number 23
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Hinkis, Arie.
Relator term author.
245 10 - TITLE STATEMENT
Title Proofs of the Cantor-Bernstein Theorem
Medium [electronic resource] :
Remainder of title A Mathematical Excursion /
Statement of responsibility, etc. by Arie Hinkis.
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Place of production, publication, distribution, manufacture Basel :
Name of producer, publisher, distributor, manufacturer Springer Basel :
-- Imprint: Birkhäuser,
Date of production, publication, distribution, manufacture, or copyright notice 2013.
300 ## - PHYSICAL DESCRIPTION
Extent XXIII, 429 p. 24 illus., 3 illus. in color.
Other physical details online resource.
336 ## - CONTENT TYPE
Content type term text
Content type code txt
Source rdacontent
337 ## - MEDIA TYPE
Media type term computer
Media type code c
Source rdamedia
338 ## - CARRIER TYPE
Carrier type term online resource
Carrier type code cr
Source rdacarrier
347 ## - DIGITAL FILE CHARACTERISTICS
File type text file
Encoding format PDF
Source rda
490 1# - SERIES STATEMENT
Series statement Science Networks. Historical Studies ;
Volume/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 Category theory (Mathematics).
Topical term or geographic name as entry element Homological algebra.
Topical term or geographic name as entry element History.
Topical term or geographic name as entry element Mathematical logic.
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
Relationship information Printed edition:
International Standard Book Number 9783034802239
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title Science Networks. Historical Studies ;
Volume number/sequential designation 45
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="http://dx.doi.org/10.1007/978-3-0348-0224-6">http://dx.doi.org/10.1007/978-3-0348-0224-6</a>
912 ## -
-- ZDB-2-SMA
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Source of classification or shelving scheme
Koha item type

No items available.