Handbook of Constructive Mathematics

doi:10.1017/9781009039888

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Catren, Gabriel 2023. Abstraction, equality and univalence. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 381, Issue. 2255,

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Restall, Greg 2025. III—What can we Mean? on Practices, Norms and Pluralisms. Proceedings of the Aristotelian Society,

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Faizrahmanov, M 2025. Computable operators on left–c.e. reals and their continuity properties. Logic Journal of the IGPL, Vol. 33, Issue. 3,

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Berger, J Bridges, Douglas Diener, Hannes and Schwichtenberg, Helmet 2025. Constructive aspects of Riemann’s permutation theorem for series. Logic Journal of the IGPL, Vol. 33, Issue. 1, p. 49.

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Edited by Douglas Bridges, University of Canterbury, Christchurch, New Zealand, Hajime Ishihara, Japan Advanced Institute of Science and Technology, Michael Rathjen, University of Leeds, Helmut Schwichtenberg, Ludwig-Maximilians-Universität Munchen

Publisher:: Cambridge University Press
Online publication date:: May 2023
Print publication year:: 2023
Online ISBN:: 9781009039888
DOI:: https://doi.org/10.1017/9781009039888

Subjects:: Mathematics (general), Mathematics, Logic, Categories and Sets, Computer Science, Programming Languages and Applied Logic
Series:: Encyclopedia of Mathematics and its Applications

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Constructive mathematics – mathematics in which 'there exists' always means 'we can construct' – is enjoying a renaissance. fifty years on from Bishop's groundbreaking account of constructive analysis, constructive mathematics has spread out to touch almost all areas of mathematics and to have profound influence in theoretical computer science. This handbook gives the most complete overview of modern constructive mathematics, with contributions from leading specialists surveying the subject's myriad aspects. Major themes include: constructive algebra and geometry, constructive analysis, constructive topology, constructive logic and foundations of mathematics, and computational aspects of constructive mathematics. A series of introductory chapters provides graduate students and other newcomers to the subject with foundations for the surveys that follow. Edited by four of the most eminent experts in the field, this is an indispensable reference for constructive mathematicians and a fascinating vista of modern constructivism for the increasing number of researchers interested in constructive approaches.

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Handbook of Constructive Mathematics

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

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Contents

Frontmatter
pp i-iv

Contents
pp v-xiii

List of Contributors
pp xiv-xv

Preface
pp xvi-xx

Part I - Introductory
pp 1-2

1 - An Introduction to Intuitionistic Logic
pp 3-19

2 - An Introduction to Constructive Set Theory: An Appetizer
pp 20-60

3 - Bishop’s Mathematics: A Philosophical Perspective
pp 61-90

Part II - Algebra and Geometry
pp 91-92

4 - Algebra in Bishop’s style: A Course in Constructive Algebra
pp 93-113

5 - Constructive Algebra: The Quillen–Suslin Theorem
pp 114-149

6 - Constructive Algebra and Point-Free Topology
pp 150-167

7 - Constructive Projective Geometry
pp 168-198

Part III - Analysis
pp 199-200

8 - Elements of Constructive Analysis
pp 201-220

9 - Constructive Functional Analysis
pp 221-254

10 - Constructive Banach Algebra Theory
pp 255-285

11 - Constructive Convex Optimisation
pp 286-301

12 - Constructive Mathematical Economics
pp 302-332

13 - A Leisurely Random Walk Down the Lane of a Constructive Theory of Stochastic Processes
pp 333-356

Part IV - Topology
pp 357-358

14 - Bases of Pseudocompact Bishop Spaces
pp 359-394

15 - Bishop Metric Spaces in Formal Topology
pp 395-425

16 - Subspaces in Pointfree Topology: Towards a New Approach to Measure Theory
pp 426-444

17 - Synthetic Topology
pp 445-482

18 - Apartness on Lattices and Between Sets
pp 483-512

Part V - Logic and Foundations
pp 513-514

19 - Countable Choice
pp 515-524

20 - The Minimalist Foundation and Bishop’s Constructive Mathematics
pp 525-563

21 - Identity, Equality, and Extensionality in Explicit Mathematics
pp 564-583

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Handbook of Constructive Mathematics

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