Proofs of the Cantor-Bernstein Theorem (Record no. 96281)
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| fixed length control field | 04451nam a22004695i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-0348-0224-6 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20140220082836.0 |
| 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 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| 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 - | |
| -- | Basel : |
| -- | Springer Basel : |
| -- | Imprint: Birkhäuser, |
| -- | 2013. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | XXIII, 429 p. 29 illus., 3 illus. in color. |
| Other physical details | online resource. |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
| -- | |
| -- | rda |
| 490 1# - SERIES STATEMENT | |
| Series statement | 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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Algebra. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Logic, Symbolic and mathematical. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | History of Mathematical Sciences. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Mathematical Logic and Foundations. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| 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 |
| 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 | http://dx.doi.org/10.1007/978-3-0348-0224-6 |
| 912 ## - | |
| -- | ZDB-2-SHU |
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