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Progress in Mathematics

Structure of Decidable Locally Finite Varieties

Authors: McKenzie, Ralph, Valeriote, Matthew

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About this book

A mathematically precise definition of the intuitive notion of "algorithm" was implicit in Kurt Godel's [1931] paper on formally undecidable propo­ sitions of arithmetic. During the 1930s, in the work of such mathemati­ cians as Alonzo Church, Stephen Kleene, Barkley Rosser and Alfred Tarski, Godel's idea evolved into the concept of a recursive function. Church pro­ posed the thesis, generally accepted today, that an effective algorithm is the same thing as a procedure whose output is a recursive function of the input (suitably coded as an integer). With these concepts, it became possible to prove that many familiar theories are undecidable (or non-recursive)-i. e. , that there does not exist an effective algorithm (recursive function) which would allow one to determine which sentences belong to the theory. It was clear from the beginning that any theory with a rich enough mathematical content must be undecidable. On the other hand, some theories with a substantial content are decidable. Examples of such decidabLe theories are the theory of Boolean algebras (Tarski [1949]), the theory of Abelian groups (Szmiele~ [1955]), and the theories of elementary arithmetic and geometry (Tarski [1951]' but Tarski discovered these results around 1930). The de­ termination of precise lines of division between the classes of decidable and undecidable theories became an important goal of research in this area. algebra we mean simply any structure (A, h(i E I)} consisting of By an a nonvoid set A and a system of finitary operations Ii over A.

Table of contents (15 chapters)

Buy this book

eBook $99.00
price for USA in USD (gross)
  • ISBN 978-1-4612-4552-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-0-8176-3439-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA in USD
  • ISBN 978-1-4612-8908-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Structure of Decidable Locally Finite Varieties
Authors
Series Title
Progress in Mathematics
Series Volume
79
Copyright
1989
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston, Inc.
eBook ISBN
978-1-4612-4552-0
DOI
10.1007/978-1-4612-4552-0
Hardcover ISBN
978-0-8176-3439-1
Softcover ISBN
978-1-4612-8908-1
Series ISSN
0743-1643
Edition Number
1
Number of Pages
VIII, 216
Topics