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From Sets and Types to Topology and Analysis: Towards practicable foundations for constructive mathematics

Online ISBN:
9780191713927
Print ISBN:
9780198566519
Publisher:
Oxford University Press
Book

From Sets and Types to Topology and Analysis: Towards practicable foundations for constructive mathematics

Laura Crosilla (ed.),
Laura Crosilla
(ed.)
Universite di Firenze
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Peter Schuster (ed.)
Peter Schuster
(ed.)
Mathematical Institut, Universitaet Munich
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Published online:
1 September 2007
Published in print:
6 October 2005
Online ISBN:
9780191713927
Print ISBN:
9780198566519
Publisher:
Oxford University Press

Abstract

Constructive mathematics is a vital area of research which has gained special attention in recent years due to the distinctive presence of computational content in its theorems. This characteristic had been already stressed by Bishop in his fundamental contribution to the subject, Foundations of Constructive Analysis (1967). Following Bishop's new approach to mathematics based on intuitionistic logic, various formal systems were introduced in the early 1970s with the intent to clarify the notion of set theory underlying his work. This book addresses the relationship between foundations and practice of constructive mathematics Bishop-style, by presenting on the one hand some very recent contributions to constructive analysis and formal topology, and on the other hand studies which underline the capabilities and expressiveness of various formal systems which have been introduced as foundations for constructive mathematics, like constructive set and type theories. The book aims to provide a point of reference by pesenting up-to-date contributions by some of the most active scholars in each field. A variety of approaches and techniques are represented to give as wide a view as possible and promote cross-fertilization between different styles and traditions. The book also aims at further promoting awareness and discussion on the issue of bridging foundations and practice of constructive mathematics, thus filling the apparent distance that has emerged between them in recent years.

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