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This work grew out of Errett Bishop's fundamental treatise 'Founda
tions of Constructive Analysis' (FCA), which appeared in 1967 and
which contained the bountiful harvest of a remarkably short period
of research by its author. Truly, FCA was an exceptional book, not
only because of the quantity of original material it contained, but
also as a demonstration of the practicability of a program which
most ma thematicians believed impossible to carry out. Errett's
book went out of print shortly after its publication, and no second
edition was produced by its publishers. Some years later, 'by a set
of curious chances', it was agreed that a new edition of FCA would
be published by Springer Verlag, the revision being carried out by
me under Errett's supervision; at the same time, Errett gener ously
insisted that I become a joint author. The revision turned out to
be much more substantial than we had anticipated, and took longer
than we would have wished. Indeed, tragically, Errett died before
the work was completed. The present book is the result of our
efforts. Although substantially based on FCA, it contains so much
new material, and such full revision and expansion of the old, that
it is essentially a new book. For this reason, and also to preserve
the integrity of the original, I decided to give our joint work a
title of its own. Most of the new material outside Chapter 5
originated with Errett."
Constructive mathematics – mathematics in which 'there exists'
always means 'we can construct' – is enjoying a renaissance.
fifty years on from Bishop's groundbreaking account of constructive
analysis, constructive mathematics has spread out to touch almost
all areas of mathematics and to have profound influence in
theoretical computer science. This handbook gives the most complete
overview of modern constructive mathematics, with contributions
from leading specialists surveying the subject's myriad aspects.
Major themes include: constructive algebra and geometry,
constructive analysis, constructive topology, constructive logic
and foundations of mathematics, and computational aspects of
constructive mathematics. A series of introductory chapters
provides graduate students and other newcomers to the subject with
foundations for the surveys that follow. Edited by four of the most
eminent experts in the field, this is an indispensable reference
for constructive mathematicians and a fascinating vista of modern
constructivism for the increasing number of researchers interested
in constructive approaches.
This is an introduction to, and survey of, the constructive
approaches to pure mathematics. The authors emphasise the viewpoint
of Errett Bishop's school, but intuitionism. Russian constructivism
and recursive analysis are also treated, with comparisons between
the various approaches included where appropriate. Constructive
mathematics is now enjoying a revival, with interest from not only
logicans but also category theorists, recursive function theorists
and theoretical computer scientists. This account for
non-specialists in these and other disciplines.
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