Proofs of the Cantor-Bernstein Theorem

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106,99 

A Mathematical Excursion, Science Networks. Historical Studies 45

ISBN: 3034802234
ISBN 13: 9783034802239
Autor: Hinkis, Arie
Verlag: Springer Basel AG
Umfang: xxiii, 429 S., 21 s/w Illustr., 3 farbige Illustr., 429 p. 24 illus., 3 illus. in color.
Erscheinungsdatum: 05.03.2013
Auflage: 1/2013
Produktform: Gebunden/Hardback
Einband: GEB

InhaltsangabePreface. – 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. 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 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.

Artikelnummer: 1598770 Kategorie:

Beschreibung

InhaltsangabePreface. - 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. 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 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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