Foundational Theories of Classical and Constructive Mathematics

Editors:

ISBN: 978-94-007-0430-5 (Print) 978-94-007-0431-2 (Online)

Table of contents (15 chapters)

  1. Front Matter

    Pages i-lxi

  2. Senses of ‘Foundations of Mathematics’

    1. Front Matter

      Pages 51-51

    2. No Access

      Book Chapter

      Pages 53-69

      Foundational Frameworks

    3. No Access

      Book Chapter

      Pages 71-84

      The Problem of Mathematical Objects

    4. No Access

      Book Chapter

      Pages 85-96

      Set Theory as a Foundation

    5. No Access

      Book Chapter

      Pages 97-110

      Foundations: Structures, Sets, and Categories

  3. Foundations of Classical Mathematics

    1. Front Matter

      Pages 111-111

    2. No Access

      Book Chapter

      Pages 113-125

      From Sets to Types, to Categories, to Sets

    3. No Access

      Book Chapter

      Pages 127-143

      Enriched Stratified Systems for the Foundations of Category Theory

    4. No Access

      Book Chapter

      Pages 145-154

      Recent Debate over Categorical Foundations

  4. Between Foundations of Classical and Foundations of Constructive Mathematics

    1. Front Matter

      Pages 155-155

    2. No Access

      Book Chapter

      Pages 157-169

      The Axiom of Choice in the Foundations of Mathematics

    3. No Access

      Book Chapter

      Pages 171-186

      Reflections on the Categorical Foundations of Mathematics

  5. Foundations of Constructive Mathematics

    1. Front Matter

      Pages 187-187

    2. No Access

      Book Chapter

      Pages 189-207

      Local Constructive Set Theory and Inductive Definitions

    3. No Access

      Book Chapter

      Pages 209-225

      Proofs and Constructions

    4. No Access

      Book Chapter

      Pages 227-243

      Euclidean Arithmetic: The Finitary Theory of Finite Sets

    5. No Access

      Book Chapter

      Pages 245-263

      Intentionality, Intuition, and Proof in Mathematics

    6. No Access

      Book Chapter

      Pages 265-310

      Foundations for Computable Topology

    7. No Access

      Book Chapter

      Pages 311-314

      Conclusion: A Perspective on Future Research in FOM