Handbook of Constructive Mathematics
Herausgeber: Bridges, Douglas; Schwichtenberg, Helmut; Rathjen, Michael; Ishihara, Hajime
Handbook of Constructive Mathematics
Herausgeber: Bridges, Douglas; Schwichtenberg, Helmut; Rathjen, Michael; Ishihara, Hajime
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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.
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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.
Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Produktdetails
- Produktdetails
- Encyclopedia of Mathematics and its Applications
- Verlag: Cambridge University Press
- Seitenzahl: 800
- Erscheinungstermin: 11. Mai 2023
- Englisch
- Abmessung: 245mm x 175mm x 53mm
- Gewicht: 1598g
- ISBN-13: 9781316510865
- ISBN-10: 1316510867
- Artikelnr.: 66454954
- Herstellerkennzeichnung
- Libri GmbH
- Europaallee 1
- 36244 Bad Hersfeld
- 06621 890
- Encyclopedia of Mathematics and its Applications
- Verlag: Cambridge University Press
- Seitenzahl: 800
- Erscheinungstermin: 11. Mai 2023
- Englisch
- Abmessung: 245mm x 175mm x 53mm
- Gewicht: 1598g
- ISBN-13: 9781316510865
- ISBN-10: 1316510867
- Artikelnr.: 66454954
- Herstellerkennzeichnung
- Libri GmbH
- Europaallee 1
- 36244 Bad Hersfeld
- 06621 890
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.
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.
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.