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Foundational Theories of Classical and Constructive Mathematics

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Cover of 'Foundational Theories of Classical and Constructive Mathematics'

Table of Contents

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    Book Overview
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    Chapter 1 Foundational Frameworks
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    Chapter 2 The Problem of Mathematical Objects
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    Chapter 3 Set Theory as a Foundation
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    Chapter 4 Foundations: Structures, Sets, and Categories
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    Chapter 5 From Sets to Types, to Categories, to Sets
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    Chapter 6 Enriched Stratified Systems for the Foundations of Category Theory
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    Chapter 7 Recent Debate over Categorical Foundations
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    Chapter 8 The Axiom of Choice in the Foundations of Mathematics
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    Chapter 9 Reflections on the Categorical Foundations of Mathematics
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    Chapter 10 Local Constructive Set Theory and Inductive Definitions
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    Chapter 11 Proofs and Constructions
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    Chapter 12 Euclidean Arithmetic: The Finitary Theory of Finite Sets
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    Chapter 13 Intentionality, Intuition, and Proof in Mathematics
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    Chapter 14 Foundations for Computable Topology
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    Chapter 15 Conclusion: A Perspective on Future Research in FOM
Attention for Chapter 2: The Problem of Mathematical Objects
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