From sets and types to topology and analysis : towards practicable foundations for constructive mathematics
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Bibliographic Information
From sets and types to topology and analysis : towards practicable foundations for constructive mathematics
（Oxford logic guides, 48）
Clarendon Press, 2005
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Includes bibliographical references and index
Description and Table of Contents
Description
This edited collection bridges the foundations and practice of constructive mathematics and focusses on the contrast between the theoretical developments, which have been most useful for computer science (eg constructive set and type theories), and more specific efforts on constructive analysis, algebra and topology. Aimed at academic logicians, mathematicians, philosophers and computer scientists Including, with contributions from leading researchers, it is
up-to-date, highly topical and broad in scope.
This is the latest volume in the Oxford Logic Guides, which also includes:
41. J.M. Dunn and G. Hardegree: Algebraic Methods in Philosophical Logic
42. H. Rott: Change, Choice and Inference: A study of belief revision and nonmonotoic reasoning
43. Johnstone: Sketches of an Elephant: A topos theory compendium, volume 1
44. Johnstone: Sketches of an Elephant: A topos theory compendium, volume 2
45. David J. Pym and Eike Ritter: Reductive Logic and Proof Search: Proof theory, semantics and control
46. D.M. Gabbay and L. Maksimova: Interpolation and Definability: Modal and Intuitionistic Logics
47. John L. Bell: Set Theory: Boolean-valued models and independence proofs, third edition
Table of Contents
- Introduction
- Errett Bishop
- 1. Generalized Inductive Definitions in Constructive Set Theory
- 2. Constructive Set Theories and their Category-theoretic Models
- 3. Presheaf models for Constructive Set Theories
- 4. Universes in Toposes
- 5. Toward a minimalistic foundation for constructive mathematics
- 6. Interactive Programs and Weakly Final Coalgebras in Dependent Type Theory
- 7. Applications of inductive definitions and choice principles to program synthesis
- 8. The duality of lcassical and constructive notions and proofs
- 9. Continuity on the real line and in formal spaces
- 10. Separation Properties in Constructive Topology
- 11. Spaces as comonoids
- 12. Predicative exponentiation of locally compact formal topologies over inductively generated ones
- 13. Some constructive roads to Tychonoff
- 14. An elementary characterisation of Krull dimension
- 15. Constructive reverse mathematics: compactness properties
- 16. Approximating integrable sets by compacts constructively
- 17. An introduction to the theory of c*-algegras in constructive mathematics
- 18. Approximations to the numerical range of an element of a Banach algebra
- 19. The constructive uniqueness of the locally convex topology on rn
- 20. Computability on Non-Separable Banach Spaces and Landau's Theorem
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