Del 45 - Science Networks. Historical Studies

Proofs of the Cantor-Bernstein Theorem

A Mathematical Excursion

Häftad, Engelska, 2015

AvArie Hinkis

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This book offers an excursion through the developmental area of research mathematics.

Produktinformation

Utgivningsdatum2015-03-07
Mått155 x 235 x 25 mm
Vikt686 g
FormatHäftad
SpråkEngelska
SerieScience Networks. Historical Studies
Antal sidor429
FörlagSpringer Basel
ISBN9783034807883

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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.