Laura Crosilla / Peter Schuster (eds.)

From Sets and Types to Topology and Analysis

Towards Practicable Foundations for Constructive Mathematics
Herausgeber: Crosilla, Laura; Schuster, Peter

• Gebundenes Buch

Produktbeschreibung

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

Produktdetails

• Verlag: Oxford University Press
• Seitenzahl: 372
• Erscheinungstermin: 8. Dezember 2005
• Englisch
• Abmessung: 242mm x 162mm x 27mm
• Gewicht: 689g
• ISBN-13: 9780198566519
• ISBN-10: 0198566514
• Artikelnr.: 21216165

Autorenporträt

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