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Real Numbers, Generalizations of the Reals, and Theories of Continua

  • Philip Ehrlich

Part of the Synthese Library book series (SYLI, volume 242)

Table of contents

  1. Front Matter
    Pages i-xxxii
  2. The Cantor-Dedekind Philosophy and Its Early Reception

    1. Front Matter
      Pages 1-1
  3. Alternative Theories of Real Numbers

    1. Front Matter
      Pages 27-27
    2. Douglas S. Bridges
      Pages 29-92
    3. J. H. Conway
      Pages 93-103
  4. Extensions and Generalizations of the Reals: The 19th-Century Geometrical Motivation

    1. Front Matter
      Pages 105-105
    2. Gordon Fisher
      Pages 107-145
    3. Henri Poincaré
      Pages 147-168
    4. Giuseppe Veronese
      Pages 169-187
  5. Extension and Generalizations of the Reals: Some 20-Century Developments

    1. Front Matter
      Pages 189-189
    2. Hourya Sinaceur
      Pages 191-206
    3. H. Jerome Keisler
      Pages 207-237
    4. Philip Ehrlich
      Pages 239-258
    5. Dieter Klaua
      Pages 259-276
  6. Back Matter
    Pages 277-288

About this book

Introduction

Since their appearance in the late 19th century, the Cantor--Dedekind theory of real numbers and philosophy of the continuum have emerged as pillars of standard mathematical philosophy. On the other hand, this period also witnessed the emergence of a variety of alternative theories of real numbers and corresponding theories of continua, as well as non-Archimedean geometry, non-standard analysis, and a number of important generalizations of the system of real numbers, some of which have been described as arithmetic continua of one type or another.
With the exception of E.W. Hobson's essay, which is concerned with the ideas of Cantor and Dedekind and their reception at the turn of the century, the papers in the present collection are either concerned with or are contributions to, the latter groups of studies. All the contributors are outstanding authorities in their respective fields, and the essays, which are directed to historians and philosophers of mathematics as well as to mathematicians who are concerned with the foundations of their subject, are preceded by a lengthy historical introduction.

Keywords

arithmetic calculus history of mathematics

Editors and affiliations

  • Philip Ehrlich
    • 1
  1. 1.Ohio UniversityUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-8248-3
  • Copyright Information Springer Science+Business Media B.V. 1994
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4362-7
  • Online ISBN 978-94-015-8248-3
  • Buy this book on publisher's site
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