From Sets And Types To Topology And Analysis: Towards practicable foundations for constructive mathematics by Laura CrosillaFrom Sets And Types To Topology And Analysis: Towards practicable foundations for constructive mathematics by Laura Crosilla

From Sets And Types To Topology And Analysis: Towards practicable foundations for constructive…

EditorLaura Crosilla, Peter Schuster

Hardcover | October 15, 2005

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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 constructiveanalysis, 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
Laura Crosilla is at Universite di Firenze. Peter Schuster is at Mathematical Institut, Universitaet Munich.
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Title:From Sets And Types To Topology And Analysis: Towards practicable foundations for constructive…Format:HardcoverDimensions:376 pages, 9.21 × 6.14 × 1.03 inPublished:October 15, 2005Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198566514

ISBN - 13:9780198566519

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Table of Contents

IntroductionDouglas Bridges: Errett Bishop1. Michael Rathjen: Generalized Inductive Definitions in Constructive Set Theory2. Alex Simpson: Constructive Set Theories and their Category-theoretic Models3. Nicola Gambino: Presheaf models for Constructive Set Theories4. Thomas Streicher: Universes in Toposes5. Maria Emilia Maietti and Giovanni Sambin: Toward a minimalistic foundation for constructive mathematics6. Peter Hancock and Anton Setzer: Interactive Programs and Weakly Final Coalgebras in Dependent Type Theory7. Ulrich Berger and Monika Seisenberger: Applications of inductive definitions and choice principles to program synthesis8. Sara Negri and Jan von Plato: The duality of lcassical and constructive notions and proofs9. Erik Palmgren: Continuity on the real line and in formal spaces10. Peter Aczel and Christopher Fox: Separation Properties in Constructive Topology11. A. Bucalo and G. Rosolini: Spaces as comonoids12. Maria Emilia Maietti: Predicative exponentiation of locally compact formal topologies over inductively generated ones13. Stephen Vickers: Some constructive roads to Tychonoff14. Thierry Coquand, Henri Lombardi and Marie-Francoise Roy: An elementary characterisation of Krull dimension15. Hajime Ishihara: Constructive reverse mathematics: compactness properties16. Bas Spitters: Approximating integrable sets by compacts constructively17. Hiroki Takamura: An introduction to the theory of c*-algegras in constructive mathematics18. Douglas Bridges and Robin Havea: Approximations to the numerical range of an element of a Banach algebra19. Douglas Bridges and Luminita Vita: The constructive uniqueness of the locally convex topology on rn20. Vasco Brattka: Computability on Non-Separable Banach Spaces and Landau's Theorem