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Reuniting the Antipodes — Constructive and Nonstandard Views of the Continuum

Symposium Proceedings, San Servolo, Venice, Italy, May 16–22, 1999

  • Peter Schuster
  • Ulrich Berger
  • Horst Osswald

Part of the Synthese Library book series (SYLI, volume 306)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Douglas Bridges, Hajime Ishihara
    Pages 25-37
  3. Evgenii I. Gordon, Olga A. Rezvova
    Pages 93-102
  4. Hajime Ishihara, Ray Mines
    Pages 103-110
  5. H. Jerome Keisler, Yeneng Sun
    Pages 111-117
  6. Boris A. Kushner
    Pages 119-126
  7. Detlef Laugwitz
    Pages 127-142
  8. Jan von Plato
    Pages 185-197
  9. Fred Richman
    Pages 199-205
  10. Fred Richman
    Pages 207-210
  11. Frank Rosemeier
    Pages 211-227
  12. Sebastiaan A. Terwijn
    Pages 271-283
  13. Back Matter
    Pages 317-329

About this book

Introduction

At first glance, Robinson's original form of nonstandard analysis appears nonconstructive in essence, because it makes a rather unrestricted use of classical logic and set theory and, in particular, of the axiom of choice. Recent developments, however, have given rise to the hope that the distance between constructive and nonstandard mathematics is actually much smaller than it appears. So the time was ripe for the first meeting dedicated simultaneously to both ways of doing mathematics – and to the current and future reunion of these seeming opposites.

Consisting of peer-reviewed research and survey articles written on the occasion of such an event, this volume offers views of the continuum from various standpoints. Including historical and philosophical issues, the topics of the contributions range from the foundations, the practice, and the applications of constructive and nonstandard mathematics, to the interplay of these areas and the development of a unified theory.

Keywords

calculus differential equation logic measure proof sequent calculus set theory

Editors and affiliations

  • Peter Schuster
    • 1
  • Ulrich Berger
    • 2
  • Horst Osswald
    • 1
  1. 1.Ludwig-Maximilians-UniversitätMünchenGermany
  2. 2.University of WalesSwanseaUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-9757-9
  • Copyright Information Springer Science+Business Media B.V. 2001
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-5885-0
  • Online ISBN 978-94-015-9757-9
  • Buy this book on publisher's site
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