E-book
Proofs of the Cantor-Bernstein Theorem [electronic resource] : A Mathematical Excursion / by Arie Hinkis.
Record details
- ISBN: 9783034802246
- Physical Description: XXIII, 429 p. 29 illus., 3 illus. in color. online resource.
- Publisher: Basel : Springer Basel : 2013.
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| Subject: | Mathematics. Algebra. Logic, Symbolic and mathematical. Mathematics. History of Mathematical Sciences. Mathematical Logic and Foundations. Category Theory, Homological Algebra. |
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Electronic resources
| 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 Russellâs Paradox | ||
| Jourdain's 1904 generalization of Grundlagen | ||
| Harward 1905 on Jourdain 1904 | ||
| Poincaré and CBT | ||
| Peano's proof of CBT | ||
| J. KÅnig'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 | ||
| SierpiÅski'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. |
