Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

Foundations of Constructive Mathematics

Metamathematical Studies

Authors: Beeson, M.J.

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About this book

This book is about some recent work in a subject usually considered part of "logic" and the" foundations of mathematics", but also having close connec­ tions with philosophy and computer science. Namely, the creation and study of "formal systems for constructive mathematics". The general organization of the book is described in the" User's Manual" which follows this introduction, and the contents of the book are described in more detail in the introductions to Part One, Part Two, Part Three, and Part Four. This introduction has a different purpose; it is intended to provide the reader with a general view of the subject. This requires, to begin with, an elucidation of both the concepts mentioned in the phrase, "formal systems for constructive mathematics". "Con­ structive mathematics" refers to mathematics in which, when you prove that l a thing exists (having certain desired properties) you show how to find it. Proof by contradiction is the most common way of proving something exists without showing how to find it - one assumes that nothing exists with the desired properties, and derives a contradiction. It was only in the last two decades of the nineteenth century that mathematicians began to exploit this method of proof in ways that nobody had previously done; that was partly made possible by the creation and development of set theory by Georg Cantor and Richard Dedekind.

Table of contents (17 chapters)

Table of contents (17 chapters)

Buy this book

eBook $109.00
price for USA in USD
  • ISBN 978-3-642-68952-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $139.99
price for USA in USD
  • ISBN 978-3-642-68954-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Foundations of Constructive Mathematics
Book Subtitle
Metamathematical Studies
Authors
Series Title
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Series Volume
6
Copyright
1985
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-68952-9
DOI
10.1007/978-3-642-68952-9
Softcover ISBN
978-3-642-68954-3
Series ISSN
0071-1136
Edition Number
1
Number of Pages
XXIII, 466
Topics