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Klappentext This edited collection bridges the foundations and practice of constructive mathematics and focuses on the contrast between the theoretical developments, which have been most useful for computer science (ie: constructive set and type theories), and more specific efforts on constructive analysis, algebra and topology. Aimed at academic logician, mathematicians, philosophers and computer scientists with contributions from leading researchers, it is up to date, highly topical and broad in scope. Zusammenfassung 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 Logic42. H. Rott: Change, Choice and Inference: A study of belief revision and nonmonotoic reasoning43. Johnstone: Sketches of an Elephant: A topos theory compendium, volume 144. Johnstone: Sketches of an Elephant: A topos theory compendium, volume 245. David J. Pym and Eike Ritter: Reductive Logic and Proof Search: Proof theory, semantics and control46. D.M. Gabbay and L. Maksimova: Interpolation and Definability: Modal and Intuitionistic Logics47. John L. Bell: Set Theory: Boolean-valued models and independence proofs, third edition Inhaltsverzeichnis Introduction Errett Bishop 1: Michael Rathjen: Generalized Inductive Definitions in Constructive Set Theory 2: Alex Simpson: Constructive Set Theories and their Category-theoretic Models 3: Nicola Gambino: Presheaf models for Constructive Set Theories 4: Thomas Streicher: Universes in Toposes 5: Maria Emilia Maietti and Giovanni Sambin: Toward a minimalistic foundation for constructive mathematics 6: Peter Hancock and Anton Setzer: Interactive Programs and Weakly Final Coalgebras in Dependent Type Theory 7: Ulrich Berger and Monika Seisenberger: Applications of inductive definitions and choice principles to program synthesis 8: Sara Negri and Jan von Plato: The duality of lcassical and constructive notions and proofs 9: Erik Palmgren: Continuity on the real line and in formal spaces 10: Peter Aczel and Christopher Fox: Separation Properties in Constructive Topology 11: A. Bucalo and G. Rosolini: Spaces as comonoids 12: Maria Emilia Maietti: Predicative exponentiation of locally compact formal topologies over inductively generated ones 13: Stephen Vickers: Some constructive roads to Tychonoff 14: Thierry Coquand, Henri Lombardi and Marie-Francoise Roy: An elementary characterisation of Krull dimension 15: Hajime Ishihara: Constructive reverse mathematics: compactness properties 16: Bas Spitters: Approximating integrable sets by compacts constructively 17: Hiroki Takamura: An introduction to the theory of c*-algegras in constructive mathematics 18: Douglas Bridges and Robin Havea: Approximations to the numerical range of an element of a Banach algebra 19: Douglas Bridges and Luminita Vita: The constructive uniqueness of the locally convex topology on rn 20: Vasco Brattka: Computability on Non-Separable Banach Spaces and Landau's Theorem ...
