Labyrinth of Thought: A History of Set Theory and Its Role in Modern Mathematics

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Birkhäuser, 22 de nov. 2013 - 440 pàgines
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"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)

 

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Continguts

The Emergence of Sets within Mathematics
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
Through the Natural Numbers to Pure Mathematics
232
Dedekind and the CantorBernstein Theorem
239
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
Logic and Type Theory in the Interwar Period
337

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
In Search of an Axiom System
297
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
Copyright

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