Proofs of the Cantor-Bernstein Theorem : A Mathematical Excursion / by Arie Hinkis
(Science Networks. Historical Studies ; 45)
| データ種別 | 電子ブック |
|---|---|
| 出版者 | Basel : Springer Basel : Imprint: Birkhäuser |
| 出版年 | 2013 |
| 本文言語 | 英語 |
| 大きさ | XXIII, 429 p. 24 illus., 3 illus. in color : online resource |
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| 内容注記 | 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 |
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| 一般注記 | 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 |
| 著者標目 | *Hinkis, Arie author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Category theory (Mathematics) LCSH:Homological algebra LCSH:History LCSH:Mathematical logic FREE:Mathematics FREE:History of Mathematical Sciences FREE:Mathematical Logic and Foundations FREE:Category Theory, Homological Algebra |
| 分 類 | DC23:510.9 |
| 巻冊次 | ISBN:9783034802246 
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| ISBN | 9783034802246 |
| URL | http://dx.doi.org/10.1007/978-3-0348-0224-6 |
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