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Hinkis, Arie

Proofs of the Cantor-Bernstein Theorem

Hinkis, Arie - Proofs of the Cantor-Bernstein Theorem, ebook

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Table of contents

Part I. Cantor and Dedekind

1. Cantor’s CBT Proof for Sets of the Power of (II)
Arie Hinkis

2. Generalizing Cantor’s CBT Proof
Arie Hinkis

3. CBT in Cantor’s 1878 Beitrag

Arie Hinkis

4. The Theory of Inconsistent Sets
Arie Hinkis

5. Comparability in Cantor’s Writings
Arie Hinkis

6. The Scheme of Complete Disjunction
Arie Hinkis

7. Ruptures in the Cantor-Dedekind Correspondence
Arie Hinkis

8. The Inconsistency of Dedekind’s Infinite Set
Arie Hinkis

9. Dedekind’s Proof of CBT
Arie Hinkis

Part II. The Early Proofs

10. Schröder’s Proof of CBT
Arie Hinkis

11. Bernstein, Borel and CBT
Arie Hinkis

12. Schoenflies’ 1900 Proof of CBT
Arie Hinkis

13. Zermelo’s 1901 Proof of CBT
Arie Hinkis

14. Bernstein’s Division Theorem
Arie Hinkis

Part III. Under the Logicist Sky

15. Russell’s 1902 Proof of CBT
Arie Hinkis

16. The Role of CBT in Russell’s Paradox
Arie Hinkis

17. Jourdain’s 1904 Generalization of Grundlagen

Arie Hinkis

18. Harward 1905 on Jourdain 1904
Arie Hinkis

19. Poincaré and CBT
Arie Hinkis

20. Peano’s Proof of CBT
Arie Hinkis

21. J. Kőnig’s Strings Gestalt
Arie Hinkis

22. From Kings to Graphs
Arie Hinkis

23. Jourdain’s Improvements Round
Arie Hinkis

24. Zermelo’s 1908 Proof of CBT
Arie Hinkis

25. Korselt’s Proof of CBT
Arie Hinkis

26. Proofs of CBT in Principia Mathematica
Arie Hinkis

27. The Origin of Hausdorff Paradox in BDT
Arie Hinkis

Part IV. At the Polish School

28. Sierpiński’s Proofs of BDT
Arie Hinkis

29. Banach’s Proof of CBT
Arie Hinkis

30. Kuratowski’s Proof of BDT
Arie Hinkis

31. Early Fixed-Point CBT Proofs: Whittaker; Tarski-Knaster
Arie Hinkis

32. CBT and BDT for Order-Types
Arie Hinkis

33. Sikorski’s Proof of CBT for Boolean Algebras
Arie Hinkis

34. Tarski’s Proofs of BDT and the Inequality-BDT
Arie Hinkis

35. Tarski’s Fixed-Point Theorem and CBT
Arie Hinkis

36. Reichbach’s Proof of CBT
Arie Hinkis

Part V. Other Ends and Beginnings

37. Hellmann’s Proof of CBT
Arie Hinkis

38. CBT and Intuitionism
Arie Hinkis

39. CBT in Category Theory
Arie Hinkis

Keywords: Mathematics, History of Mathematical Sciences, Mathematical Logic and Foundations, Category Theory, Homological Algebra

Author(s)
Publisher
Springer
Publication year
2013
Language
en
Edition
2013
Series
Science Networks. Historical Studies
Page amount
23 pages
Category
Natural Sciences
Format
Ebook
eISBN (PDF)
9783034802246

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