2007

Labyrinth of Thought

A History of Set Theory and Its Role in Modern Mathematics

Authors:

ISBN: 978-3-7643-8349-7 (Print) 978-3-7643-8350-3 (Online)

Table of contents (11 chapters)

  1. Front Matter

    Pages i-xxv

  2. The Emergence of Sets within Mathematics

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 4-38

      Institutional and Intellectual Contexts in German Mathematics, 1800–1870

    3. No Access

      Book Chapter

      Pages 39-80

      A New Fundamental Notion: Riemann’s Manifolds

    4. No Access

      Book Chapter

      Pages 81-116

      Dedekind and the Set-theoretical Approach to Algebra

    5. No Access

      Book Chapter

      Pages 117-144

      The Real Number System

    6. No Access

      Book Chapter

      Pages 145-168

      Origins of the Theory of Point-Sets

  3. Entering the Labyrinth-Toward Abstract Set Theory

    1. Front Matter

      Pages 169-169

    2. No Access

      Book Chapter

      Pages 171-214

      The Notion of Cardinality and the Continuum Hypothesis

    3. No Access

      Book Chapter

      Pages 215-255

      Sets and Maps as a Foundation for Mathematics

    4. No Access

      Book Chapter

      Pages 257-296

      The Transfinite Ordinals and Cantor’s Mature Theory

  4. In Search of an Axiom System

    1. Front Matter

      Pages 297-298

    2. No Access

      Book Chapter

      Pages 299-336

      Diffusion, Crisis, and Bifurcation: 1890 to 1914

    3. No Access

      Book Chapter

      Pages 337-364

      Logic and Type Theory in the Interwar Period

    4. No Access

      Book Chapter

      Pages 365-392

      Consolidation of Axiomatic Set Theory

  5. Back Matter

    Pages 393-466