Proofs of the Cantor-Bernstein Theorem

A Mathematical Excursion

Authors:

ISBN: 978-3-0348-0223-9 (Print) 978-3-0348-0224-6 (Online)

Table of contents (39 chapters)

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  1. Front Matter

    Pages i-xxiii

  2. Cantor and Dedekind

    1. Front Matter

      Pages 1-1

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      Book Chapter

      Pages 3-14

      Cantor’s CBT Proof for Sets of the Power of (II)

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      Book Chapter

      Pages 15-25

      Generalizing Cantor’s CBT Proof

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      Book Chapter

      Pages 27-38

      CBT in Cantor’s 1878 Beitrag

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      Book Chapter

      Pages 39-47

      The Theory of Inconsistent Sets

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      Book Chapter

      Pages 49-55

      Comparability in Cantor’s Writings

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      Book Chapter

      Pages 57-66

      The Scheme of Complete Disjunction

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      Book Chapter

      Pages 67-75

      Ruptures in the Cantor-Dedekind Correspondence

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      Book Chapter

      Pages 77-86

      The Inconsistency of Dedekind’s Infinite Set

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      Book Chapter

      Pages 87-101

      Dedekind’s Proof of CBT

  3. The Early Proofs

    1. Front Matter

      Pages 103-103

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      Book Chapter

      Pages 105-116

      Schröder’s Proof of CBT

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      Book Chapter

      Pages 117-124

      Bernstein, Borel and CBT

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      Book Chapter

      Pages 125-128

      Schoenflies’ 1900 Proof of CBT

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      Book Chapter

      Pages 129-138

      Zermelo’s 1901 Proof of CBT

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      Book Chapter

      Pages 139-152

      Bernstein’s Division Theorem

  4. Under the Logicist Sky

    1. Front Matter

      Pages 153-153

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      Book Chapter

      Pages 155-163

      Russell’s 1902 Proof of CBT

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      Book Chapter

      Pages 165-170

      The Role of CBT in Russell’s Paradox

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      Book Chapter

      Pages 171-184

      Jourdain’s 1904 Generalization of Grundlagen

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      Book Chapter

      Pages 185-193

      Harward 1905 on Jourdain 1904

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      Book Chapter

      Pages 195-208

      Poincaré and CBT

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      Book Chapter

      Pages 209-215

      Peano’s Proof of CBT

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