Labyrinth of Thought

One: The Emergence of Sets within Mathematics.- I Institutional and Intellectual Contexts in German Mathematics, 1800–1870.- II A New Fundamental Notion: Riemann’s Manifolds.- III Dedekind and the Set-theoretical Approach to Algebra.- IV The Real Number System.- V Origins of the Theory of Point-Sets.- Two: Entering the Labyrinth — Toward Abstract Set Theory.- VI The Notion of Cardinality and the Continuum Hypothesis.- VII Sets and Maps as a Foundation for Mathematics.- VIII The Transfinite Ordinals and Cantor’s Mature Theory.- Three: In Search of an Axiom System.- IX Diffusion, Crisis, and Bifurcation: 1890 to 1914.- X Logic and Type Theory in the Interwar Period.- XI Consolidation of Axiomatic Set Theory.- Bibliographical References.- Index of Illustrations.- Name Index.