Logic: From Foundations to Applications European Logic Colloquium

by Hodges, Wilfrid; Hyland, Martin; Steinhorn, Charles; Truss, John

• ISBN13: 9780198538622
• ISBN10: 0198538626
• Format: Hardcover
• Copyright: 1996-08-22
• Publisher: Clarendon Press

Summary

This book contains twenty-one essays by leading authorities on aspects of contemporary logic, ranging from foundations of set theory to applications of logic in computing and in the theory of fields.In those parts of logic closest to computer science, the gap between foundations and applications is often small, as illustrated by three essays on the proof theory of non-classical logics. There are also chapters on the lambda calculus, on relating logic programs to inductive definitions, onBuechi and Presburger arithmetics, and on definability in Lindenbaum algebras. Aspects of constructive mathematics discussed are embeddings of Heyting algebras and proofs in mathematical anslysis.Set theory is well covered with six chapters discussing Cohen forcing, Baire category, determinancy, Nash-Williams theory, critical points (and the remarkable connection between them and properties of left distributive operations) and independent structures. The longest chapter in the book is a survey of 0-minimal structures, by Lou van den Dries; during the last ten years these structures have come to take a central place in applications of model theory to fields and function theory, and this chapter is the first broad survey of the area. Otherchapters illustrate how to apply model theory to field theory, complex geometry and groups, and how to recover from its automorphism group. Finally, one chapter applies to the theory of toric varieties to solve problems about many-valued logics.

Table of Contents

The method of hypersequents in the proof theory of propositional non-classical logic

Church-Rosser lambda theories, infinite lambda-terms and consistency problems

Baire category for monotone sets

Equality in substructural logics

Substructural predicates

Critical points in an algebra of elementary embeddings II

0-minimality and tame topology

Embeddings of Heyting algebras

Embedding normal forms

Analysing proofs in analysis

Subalgebras of Cohen Algebras need not be Cohen

Independence structures in set theory

Recovering the action of an automorphism group

On the logical strength of Nash-Williams' theorem on transfinite sequences

Open questions around Buchi and Presburger arithmetics

A growth dichotomy for 0-minimal expansions of ordered fields

Lukasiewicz normal forms and toric desingularizations

From logic problems to inductive definitions

Hyperstable theories

Quasi-Riemann Surfaces

Table of Contents provided by Publisher. All Rights Reserved.