This handbook gives a complete overview of modern constructive mathematics - mathematics in which 'there exists' always means 'we can construct' - and its applications. Written and edited by leading experts, it is an indispensable reference for established constructive mathematicians and guide to the field for graduate students and other newcomers.
This handbook gives a complete overview of modern constructive mathematics - mathematics in which 'there exists' always means 'we can construct' - and its applications. Written and edited by leading experts, it is an indispensable reference for established constructive mathematicians and guide to the field for graduate students and other newcomers.
Preface Douglas Bridges, Hajime Ishihara, Michael Rathjen and Helmut Schwichtenberg Part I. Introductory: 1. Introduction to intuitionistic logic Michael Rathjen 2. Introduction to CZF: an appetizer Michael Rathjen 3. Bishop's mathematics: a philosophical perspective Laura Crosilla Part II. Algebra and Geometry: 4. Algebra in Bishop's style: a course in constructive algebra Henri Lombardi 5. Constructive algebra: the Quillen-Suslin theorem Ihsen Yengui 6. Constructive algebra and point-free topology Thierry Coquand 7. Constructive projective geometry Mark Mandelkern Part III. Analysis: 8. Elements of constructive analysis Hajime Ishihara 9. Constructive functional analysis Hajime Ishihara 10. Constructive Banach algebra theory Robin Havea and Douglas Bridges 11. Constructive convex optimization Josef Berger and Gregor Svindland 12. Constructive mathematical economics Matthew Hendtlass and Douglas Bridges 13. Constructive stochastic processes Yuen-Kwok Chan Part IV. Topology: 14. Bases of pseudocompact Bishop spaces Iosif Petrakis 15. Bishop metric spaces in formal topology Tatsuji Kawai 16. Subspaces in point free topology and measure theory Francesco Ciraulo 17. Synthetic topology Davorin Lenik 18. Apartness on lattices and between sets Douglas Bridges Part V. Logic and Foundations: 19. Countable choice Fred Richman 20. The Minimalist Foundation and Bishop's constructive mathematics Maria Maietti, Giovanni Sambin 21. Identity, equality, and extensionality in explicit mathematics Gerhard Jäger 22. Inner and outer models for constructive set theories Robert Lubarsky 23. An introduction to constructive reverse mathematics Hajime Ishihara 24. Systems for constructive reverse mathematics Takako Nemoto 25. Brouwer's fan theorem Josef Berger Part VI. Aspects of Computation: 26. Computational aspects of Bishop's constructive mathematics Helmut Schwichtenberg 27. Application of constructive analysis in exact real arithmetic Kenji Miyamoto 28. Efficient algorithms from proofs in constructive analysis Mark Bickford 29. On the computational content of choice principles Ulrich Berger and Monika Seisenberger Index.
Preface Douglas Bridges, Hajime Ishihara, Michael Rathjen and Helmut Schwichtenberg Part I. Introductory: 1. Introduction to intuitionistic logic Michael Rathjen 2. Introduction to CZF: an appetizer Michael Rathjen 3. Bishop's mathematics: a philosophical perspective Laura Crosilla Part II. Algebra and Geometry: 4. Algebra in Bishop's style: a course in constructive algebra Henri Lombardi 5. Constructive algebra: the Quillen-Suslin theorem Ihsen Yengui 6. Constructive algebra and point-free topology Thierry Coquand 7. Constructive projective geometry Mark Mandelkern Part III. Analysis: 8. Elements of constructive analysis Hajime Ishihara 9. Constructive functional analysis Hajime Ishihara 10. Constructive Banach algebra theory Robin Havea and Douglas Bridges 11. Constructive convex optimization Josef Berger and Gregor Svindland 12. Constructive mathematical economics Matthew Hendtlass and Douglas Bridges 13. Constructive stochastic processes Yuen-Kwok Chan Part IV. Topology: 14. Bases of pseudocompact Bishop spaces Iosif Petrakis 15. Bishop metric spaces in formal topology Tatsuji Kawai 16. Subspaces in point free topology and measure theory Francesco Ciraulo 17. Synthetic topology Davorin Lenik 18. Apartness on lattices and between sets Douglas Bridges Part V. Logic and Foundations: 19. Countable choice Fred Richman 20. The Minimalist Foundation and Bishop's constructive mathematics Maria Maietti, Giovanni Sambin 21. Identity, equality, and extensionality in explicit mathematics Gerhard Jäger 22. Inner and outer models for constructive set theories Robert Lubarsky 23. An introduction to constructive reverse mathematics Hajime Ishihara 24. Systems for constructive reverse mathematics Takako Nemoto 25. Brouwer's fan theorem Josef Berger Part VI. Aspects of Computation: 26. Computational aspects of Bishop's constructive mathematics Helmut Schwichtenberg 27. Application of constructive analysis in exact real arithmetic Kenji Miyamoto 28. Efficient algorithms from proofs in constructive analysis Mark Bickford 29. On the computational content of choice principles Ulrich Berger and Monika Seisenberger Index.
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