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Computability and Models

Perspectives East and West

  • S. Barry Cooper
  • Sergey S. Goncharov

Part of the The University Series in Mathematics book series (USMA)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Serikzhan Badaev, Sergey Goncharov, Andrea Sorbi
    Pages 11-44
  3. Serikzhan Badaev, Sergey Goncharov, Sergey Podzorov, Andrea Sorbi
    Pages 45-77
  4. Serikzhan Badaev, Sergey Goncharov, Andrea Sorbi
    Pages 79-91
  5. Vasco Brattka
    Pages 93-136
  6. S. Barry Cooper, Piergiorgio Odifreddi
    Pages 137-160
  7. William Gasarch
    Pages 161-195
  8. Eberhard Herrmann
    Pages 197-214
  9. Sanjay Jain, Frank Stephan
    Pages 215-247
  10. Iskander Kalimullin
    Pages 249-258
  11. Steffen Lempp, Andrei S. Morozov, Charles F. D. McCoy, D. Reed Solomon
    Pages 259-265
  12. Roland Sh. Omanadze
    Pages 289-319
  13. Victor Selivanov
    Pages 321-350
  14. Back Matter
    Pages 371-375

About this book

Introduction

Science involves descriptions of the world we live in. It also depends on nature exhibiting what we can best describe as a high aLgorithmic content. The theme running through this collection of papers is that of the interaction between descriptions, in the form of formal theories, and the algorithmic content of what is described, namely of the modeLs of those theories. This appears most explicitly here in a number of valuable, and substantial, contributions to what has until recently been known as 'recursive model theory' - an area in which researchers from the former Soviet Union (in particular Novosibirsk) have been pre-eminent. There are also articles concerned with the computability of aspects of familiar mathematical structures, and - a return to the sort of basic underlying questions considered by Alan Turing in the early days of the subject - an article giving a new perspective on computability in the real world. And, of course, there are also articles concerned with the classical theory of computability, including the first widely available survey of work on quasi-reducibility. The contributors, all internationally recognised experts in their fields, have been associated with the three-year INTAS-RFBR Research Project "Com­ putability and Models" (Project No. 972-139), and most have participated in one or more of the various international workshops (in Novosibirsk, Heidelberg and Almaty) and otherresearch activities of the network.

Keywords

Arithmetic Division Permutation addition computability modeling

Authors and affiliations

  • S. Barry Cooper
    • 1
  • Sergey S. Goncharov
    • 2
  1. 1.University of LeedsLeedsUK
  2. 2.Novosibirsk State UniversityNovosibirskRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4615-0755-0
  • Copyright Information Kluwer Academic / Plenum Publishers, New York 2003
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-5225-9
  • Online ISBN 978-1-4615-0755-0
  • Buy this book on publisher's site