Proofs of the Cantor-Bernstein Theorem: A Mathematical Excursion - Softcover

Hinkis, Arie

Softcover

ISBN 10: 3034802250 ISBN 13: 9783034802253

Publisher: Birkhäuser, 2013

Synopsis

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.

Edition details

• Publisher: Birkhäuser
• Publication date: 2013
• ISBN 10: 3034802250
• ISBN 13: 9783034802253
• Binding: Paperback
• Language: English