University Series in Mathematics

Computability and Models

Perspectives East and West

Editors: Cooper, Barry S., Goncharov, Sergey (Eds.)

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About this book

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.

Table of contents (15 chapters)

  • Truth-Table Complete Computably Enumerable Sets

    Arslanov, Marat M.

    Pages 1-10

  • Completeness and Universality of Arithmetical Numberings

    Badaev, Serikzhan (et al.)

    Pages 11-44

  • Algebraic Properties of Rogers Semilattices of Arithmetical Numberings

    Badaev, Serikzhan (et al.)

    Pages 45-77

  • Isomorphism Types and Theories of Rogers Semilattices of Arithmetical Numberings

    Badaev, Serikzhan (et al.)

    Pages 79-91

  • Computability over Topological Structures

    Brattka, Vasco

    Pages 93-136

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-1-4615-0755-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $189.00
price for USA
  • ISBN 978-0-306-47400-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $189.00
price for USA
  • ISBN 978-1-4613-5225-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Computability and Models
Book Subtitle
Perspectives East and West
Editors
  • Barry S. Cooper
  • Sergey Goncharov
Series Title
University Series in Mathematics
Copyright
2003
Publisher
Springer US
Copyright Holder
Kluwer Academic / Plenum Publishers, New York
eBook ISBN
978-1-4615-0755-0
DOI
10.1007/978-1-4615-0755-0
Hardcover ISBN
978-0-306-47400-2
Softcover ISBN
978-1-4613-5225-9
Edition Number
1
Number of Pages
XIX, 375
Topics