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.
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.
Edited by Laura Crosilla, Universite di Firenze and Peter Schuster, Mathematical Institut, Universitaet Munich
Contributors: Douglas Bridges Michael Rathjen Alex Simpson Nicola Gambino Thomas Streicher Maria Emilia Maietti Giovanni Sambin Peter Hancock Anton Setzer Ulrich Berger Monika Seisenberger Sara Negri Jan von Plato Erik Palmgren Peter Aczel Christopher Fox A. Bucalo G. Rosolini Stephen Vickers Thierry Coquand Henri Lombardi Marie-Francoise Roy Hajime Ishihara Bas Spitters Hiroki Takamura Robin Havea Luminita Vita Vasco Brattka
Inhaltsangabe
* 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
* 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
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