Proofs of the Cantor-Bernstein Theorem

Part I. Cantor and Dedekind

1. Cantor’s CBT Proof for Sets of the Power of (II)
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2. Generalizing Cantor’s CBT Proof
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3. CBT in Cantor’s 1878 Beitrag

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4. The Theory of Inconsistent Sets
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5. Comparability in Cantor’s Writings
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6. The Scheme of Complete Disjunction
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7. Ruptures in the Cantor-Dedekind Correspondence
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8. The Inconsistency of Dedekind’s Infinite Set
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9. Dedekind’s Proof of CBT
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Part II. The Early Proofs

10. Schröder’s Proof of CBT
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11. Bernstein, Borel and CBT
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12. Schoenflies’ 1900 Proof of CBT
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13. Zermelo’s 1901 Proof of CBT
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14. Bernstein’s Division Theorem
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Part III. Under the Logicist Sky

15. Russell’s 1902 Proof of CBT
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16. The Role of CBT in Russell’s Paradox
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17. Jourdain’s 1904 Generalization of Grundlagen

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18. Harward 1905 on Jourdain 1904
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19. Poincaré and CBT
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20. Peano’s Proof of CBT
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21. J. Kőnig’s Strings Gestalt
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22. From Kings to Graphs
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23. Jourdain’s Improvements Round
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24. Zermelo’s 1908 Proof of CBT
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25. Korselt’s Proof of CBT
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26. Proofs of CBT in Principia Mathematica
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27. The Origin of Hausdorff Paradox in BDT
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Part IV. At the Polish School

28. Sierpiński’s Proofs of BDT
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29. Banach’s Proof of CBT
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30. Kuratowski’s Proof of BDT
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31. Early Fixed-Point CBT Proofs: Whittaker; Tarski-Knaster
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32. CBT and BDT for Order-Types
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33. Sikorski’s Proof of CBT for Boolean Algebras
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34. Tarski’s Proofs of BDT and the Inequality-BDT
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35. Tarski’s Fixed-Point Theorem and CBT
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36. Reichbach’s Proof of CBT
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Part V. Other Ends and Beginnings

37. Hellmann’s Proof of CBT
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38. CBT and Intuitionism
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39. CBT in Category Theory
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Keywords: Mathematics, History of Mathematical Sciences, Mathematical Logic and Foundations, Category Theory, Homological Algebra