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Logic: From Foundations to Applications - European Logic Colloquium (Hardcover)
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Logic: From Foundations to Applications - European Logic Colloquium (Hardcover)
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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, on Buechi 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. Other chapters 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.
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