Labyrinth of Thought: A History of Set Theory and Its Role in Modern MathematicsBirkhäuser, 22 de nov. 2013 - 440 pàgines "José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic) |
Continguts
1 | |
Riemanns Manifolds | 39 |
Dedekind and the Settheoretical Approach to Algebra | 81 |
The Real Number System | 117 |
Origins of the Theory of PointSets | 145 |
Entering the Labyrinth | 169 |
Sets and Maps as a Foundation for Mathematics | 215 |
Through the Natural Numbers to Pure Mathematics | 232 |
In Search of an Axiom System | 297 |
1890 to 1914 | 299 |
Spreading Set Theory | 300 |
The Complex Emergence of the Paradoxes | 306 |
The Axiom of Choice and the Early Foundational Debate | 311 |
The Early Work of Zermelo | 317 |
Russells Theory of Types | 325 |
Other Developments in Set Theory | 333 |
Dedekind and the CantorBernstein Theorem | 239 |
Dedekinds Theorem of Infinity and Epistemology | 241 |
Reception of Dedekinds Ideas | 248 |
The Transfinite Ordinals and Cantors Mature Theory 257 | 256 |
Free Mathematics | 259 |
Cantors Notion of Set in the Early 1880s | 263 |
The Transfinite Ordinal Numbers | 267 |
Ordered Sets | 274 |
The Reception in the Early 1880s | 282 |
Cantors Theorem | 286 |
The Beiträge zur Begründung der transfiniten Mengenlehre | 288 |
Cantor and the Paradoxes | 290 |
Logic and Type Theory in the Interwar Period | 337 |
Weyl Brouwer Hilbert | 338 |
Diverging Conceptions of Logic | 345 |
The Road to the Simple Theory of Types | 348 |
Type Theory at its Zenith | 353 |
Weyl and Skolem on FirstOrder Logic | 357 |
Consolidation of Axiomatic Set Theory | 365 |
The Contributions of Fraenkel | 366 |
Bibliographical References | 393 |
Index of Illustrations | 422 |
Subject Index | 430 |
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Labyrinth of Thought: A History of Set Theory and Its Role in Modern Mathematics José Ferreirós Previsualització no disponible - 2009 |