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Logicism, Intuitionism, and Formalism

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Cover of 'Logicism, Intuitionism, and Formalism'

Table of Contents

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    Book Overview
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    Chapter 1 Introduction: The Three Foundational Programmes
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    Chapter 2 Protocol Sentences for Lite Logicism
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    Chapter 3 Frege’s Context Principle and Reference to Natural Numbers
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    Chapter 4 The Measure of Scottish Neo-Logicism
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    Chapter 5 Natural Logicism via the Logic of Orderly Pairing
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    Chapter 6 A Constructive Version of the Lusin Separation Theorem
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    Chapter 7 Dini’s Theorem in the Light of Reverse Mathematics
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    Chapter 8 Journey into Apartness Space
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    Chapter 9 Relativization of Real Numbers to a Universe
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    Chapter 10 100 Years of Zermelo’s Axiom of Choice: What was the Problem with It?
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    Chapter 11 Intuitionism and the Anti-Justification of Bivalence
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    Chapter 12 From Intuitionistic to Point-Free Topology: On the Foundation of Homotopy Theory
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    Chapter 13 Program Extraction in Constructive Analysis
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    Chapter 14 Brouwer’s Approximate Fixed-Point Theorem is Equivalent to Brouwer’s Fan Theorem
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    Chapter 15 “Gödel’s Modernism: On Set-Theoretic Incompleteness,” Revisited
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    Chapter 16 Tarski’s Practice and Philosophy: Between Formalism and Pragmatism
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    Chapter 17 The Constructive Hilbert Program and the Limits of Martin-Löf Type Theory
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    Chapter 18 Categories, Structures, and the Frege-Hilbert Controversy: The Status of Meta-mathematics
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    Chapter 19 Beyond Hilbert’s Reach?
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    Chapter 20 Hilbert and the Problem of Clarifying the Infinite
Attention for Chapter 10: 100 Years of Zermelo’s Axiom of Choice: What was the Problem with It?
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Chapter title
100 Years of Zermelo’s Axiom of Choice: What was the Problem with It?
Chapter number 10
Book title
Logicism, Intuitionism, and Formalism
Published by
Springer, Dordrecht, January 2009
DOI 10.1007/978-1-4020-8926-8_10
Book ISBNs
978-1-4020-8925-1, 978-1-4020-8926-8
Authors

Per Martin-Löf, Martin-Löf, Per

Mendeley readers

Mendeley readers

The data shown below were compiled from readership statistics for 20 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
United Kingdom 1 5%
Switzerland 1 5%
Unknown 18 90%

Demographic breakdown

Readers by professional status Count As %
Student > Ph. D. Student 6 30%
Researcher 5 25%
Other 3 15%
Student > Bachelor 1 5%
Student > Master 1 5%
Other 1 5%
Unknown 3 15%
Readers by discipline Count As %
Computer Science 5 25%
Philosophy 3 15%
Mathematics 2 10%
Business, Management and Accounting 1 5%
Linguistics 1 5%
Other 5 25%
Unknown 3 15%