Proofs of the Cantor-Bernstein Theorem A Mathematical Excursion /

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Hinkis, Arie (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Basel : Springer Basel : Imprint: Birkhäuser, 2013.
Edición:1st ed. 2013.
Colección:Science Networks. Historical Studies, 45
Temas:
Mathematics.
History.
Mathematical logic.
Algebra, Homological.
History of Mathematical Sciences.
Mathematical Logic and Foundations.
Category Theory, Homological Algebra.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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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