eBook ISBN:  9780821876947 
Product Code:  CONM/106.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821876947 
Product Code:  CONM/106.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 106; 1990; 297 ppMSC: Primary 58; 03; Secondary 46
This volume contains the proceedings of the Workshop on Logic and Computation, held in July 1987 at CarnegieMellon 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 settheoretic 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 secondorder 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 smashbased hierarchy between PTIME and PSPACE (preliminary version) [ MR 1057817 ]

Solomon Feferman — Polymorphic typed lambdacalculi in a typefree 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 mixedtime [ 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 — RadonNikodým theorem is equivalent to arithmetical comprehension [ MR 1057829 ]


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This volume contains the proceedings of the Workshop on Logic and Computation, held in July 1987 at CarnegieMellon 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 settheoretic 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 secondorder 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 smashbased hierarchy between PTIME and PSPACE (preliminary version) [ MR 1057817 ]

Solomon Feferman — Polymorphic typed lambdacalculi in a typefree 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 mixedtime [ 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 — RadonNikodým theorem is equivalent to arithmetical comprehension [ MR 1057829 ]