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Logic and Computation
Edited by: Wilfried Sieg
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Contemporary Mathematics
1990; 297 pp; softcover
Volume: 106
ISBN-10: 0-8218-5110-1
ISBN-13: 978-0-8218-5110-4
List Price: US$49
Member Price: US$39.20
Order Code: CONM/106
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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

  • M. Beeson -- Some theories conservative over intuitionistic arithmetic
  • G. Bellin -- Ramsey interpreted: A parametric version of Ramsey's theorem
  • D. K. Brown -- Notions of closed subsets of a complete separable metric space in weak subsystems of second order arithmetic
  • W. Buchholz and W. Sieg -- A note on polynomial time computable arithmetic
  • S. R. Buss -- Axiomatizations and conservation results for fragments of bounded arithmetic
  • P. G. Clote -- A smash-based hierarchy between PTIME and PSPACE
  • S. Feferman -- Polymorphic typed lambda-calculi in a type-free axiomatic framework
  • F. Ferreira -- Polynomial time computable arithmetic
  • C. Goad -- Metaprogramming in SIL
  • K. Hatzikiriakou and S. G. Simpson -- \(WKL_0\) and orderings of countable Abelian groups
  • J. L. Hirst -- Marriage theorems and reverse mathematics
  • D. Leivant -- Computationally based set existence principles
  • K. McAloon -- Hierarchy results for MIXED-TIME
  • A. Nerode and J. B. Remmel -- Polynomial time equivalence types
  • F. Pfenning -- Program development through proof transformation
  • R. Statman -- Some models of Scott's theory \(LCF\) based on a notion of rate of convergence
  • G. Takeuti -- Sharply bounded arithmetic and the function \(a\dot-1\)
  • X. Yu -- Radon-Nikodym Theorem is equivalent to arithmetical comprehension
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