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Logic and Computation
 
Edited by: Wilfried Sieg Carnegie Mellon University, Pittsburgh, A
Logic and Computation
eBook ISBN:  978-0-8218-7694-7
Product Code:  CONM/106.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Logic and Computation
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Logic and Computation
Edited by: Wilfried Sieg Carnegie Mellon University, Pittsburgh, A
eBook ISBN:  978-0-8218-7694-7
Product Code:  CONM/106.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 1061990; 297 pp
    MSC: Primary 58; 03; Secondary 46;

    This volume contains the proceedings of the Workshop on Logic and Computation, held in July 1987 at Carnegie-Mellon University. The focus of the workshop was the refined interaction between mathematics and computation theory, one of the most fascinating and potentially fruitful developments in logic. The importance of this interaction lies not only in the emergence of the computer as a powerful tool in mathematics research, but also in the various attempts to carry out significant parts of mathematics in computationally informative ways.

    The proceedings pursue three complementary aims: to develop parts of mathematics under minimal set-theoretic assumptions; to provide formal frameworks suitable for computer implementation; and to extract, from formal proofs, mathematical and computational information. Aimed at logicians, mathematicians, and computer scientists, this volume is rich in results and replete with mathematical, logical, and computational problems.

  • Table of Contents
     
     
    • Articles
    • Michael Beeson — Some theories conservative over intuitionistic arithmetic [ MR 1057812 ]
    • Gianluigi Bellin — Ramsey interpreted: a parametric version of Ramsey’s theorem [ MR 1057813 ]
    • Douglas K. Brown — Notions of closed subsets of a complete separable metric space in weak subsystems of second-order arithmetic [ MR 1057814 ]
    • Wilfried Buchholz and Wilfried Sieg — A note on polynomial time computable arithmetic [ MR 1057815 ]
    • Samuel R. Buss — Axiomatizations and conservation results for fragments of bounded arithmetic [ MR 1057816 ]
    • Peter G. Clote — A smash-based hierarchy between PTIME and PSPACE (preliminary version) [ MR 1057817 ]
    • Solomon Feferman — Polymorphic typed lambda-calculi in a type-free axiomatic framework [ MR 1057818 ]
    • Fernando Ferreira — Polynomial time computable arithmetic [ MR 1057819 ]
    • Chris Goad — Metaprogramming in SIL
    • Kostas Hatzikiriakou and Stephen G. Simpson — ${\rm WKL}_0$ and orderings of countable abelian groups [ MR 1057821 ]
    • Jeffry L. Hirst — Marriage theorems and reverse mathematics [ MR 1057822 ]
    • Daniel Leivant — Computationally based set existence principles [ MR 1057823 ]
    • Ken McAloon — Hierarchy results for mixed-time [ MR 1057824 ]
    • A. Nerode and J. B. Remmel — Polynomial time equivalence types [ MR 1057825 ]
    • Frank Pfenning — Program development through proof transformation [ MR 1057826 ]
    • Rick Statman — Some models of Scott’s theory ${\rm LCF}$ based on a notion of rate of convergence [ MR 1057827 ]
    • Gaisi Takeuti — Sharply bounded arithmetic and the function $a \stackrel {.}{-} 1$ [ MR 1057828 ]
    • Xiaokang Yu — Radon-Nikodým theorem is equivalent to arithmetical comprehension [ MR 1057829 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1061990; 297 pp
MSC: Primary 58; 03; Secondary 46;

This volume contains the proceedings of the Workshop on Logic and Computation, held in July 1987 at Carnegie-Mellon University. The focus of the workshop was the refined interaction between mathematics and computation theory, one of the most fascinating and potentially fruitful developments in logic. The importance of this interaction lies not only in the emergence of the computer as a powerful tool in mathematics research, but also in the various attempts to carry out significant parts of mathematics in computationally informative ways.

The proceedings pursue three complementary aims: to develop parts of mathematics under minimal set-theoretic assumptions; to provide formal frameworks suitable for computer implementation; and to extract, from formal proofs, mathematical and computational information. Aimed at logicians, mathematicians, and computer scientists, this volume is rich in results and replete with mathematical, logical, and computational problems.

  • Articles
  • Michael Beeson — Some theories conservative over intuitionistic arithmetic [ MR 1057812 ]
  • Gianluigi Bellin — Ramsey interpreted: a parametric version of Ramsey’s theorem [ MR 1057813 ]
  • Douglas K. Brown — Notions of closed subsets of a complete separable metric space in weak subsystems of second-order arithmetic [ MR 1057814 ]
  • Wilfried Buchholz and Wilfried Sieg — A note on polynomial time computable arithmetic [ MR 1057815 ]
  • Samuel R. Buss — Axiomatizations and conservation results for fragments of bounded arithmetic [ MR 1057816 ]
  • Peter G. Clote — A smash-based hierarchy between PTIME and PSPACE (preliminary version) [ MR 1057817 ]
  • Solomon Feferman — Polymorphic typed lambda-calculi in a type-free axiomatic framework [ MR 1057818 ]
  • Fernando Ferreira — Polynomial time computable arithmetic [ MR 1057819 ]
  • Chris Goad — Metaprogramming in SIL
  • Kostas Hatzikiriakou and Stephen G. Simpson — ${\rm WKL}_0$ and orderings of countable abelian groups [ MR 1057821 ]
  • Jeffry L. Hirst — Marriage theorems and reverse mathematics [ MR 1057822 ]
  • Daniel Leivant — Computationally based set existence principles [ MR 1057823 ]
  • Ken McAloon — Hierarchy results for mixed-time [ MR 1057824 ]
  • A. Nerode and J. B. Remmel — Polynomial time equivalence types [ MR 1057825 ]
  • Frank Pfenning — Program development through proof transformation [ MR 1057826 ]
  • Rick Statman — Some models of Scott’s theory ${\rm LCF}$ based on a notion of rate of convergence [ MR 1057827 ]
  • Gaisi Takeuti — Sharply bounded arithmetic and the function $a \stackrel {.}{-} 1$ [ MR 1057828 ]
  • Xiaokang Yu — Radon-Nikodým theorem is equivalent to arithmetical comprehension [ MR 1057829 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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