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...
| Κύριος συγγραφέας: | |
|---|---|
| Συγγραφή απο Οργανισμό/Αρχή: | |
| Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
| Γλώσσα: | English |
| Έκδοση: |
Basel :
Springer Basel : Imprint: Birkhäuser,
2013.
|
| Σειρά: | Science Networks. Historical Studies ;
45 |
| Θέματα: | |
| Διαθέσιμο Online: | Full Text via HEAL-Link |
Πίνακας περιεχομένων:
- 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.
