Logic: from foundations to applications : European logic colloquium, Volume 1993
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.
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ChurchRosser Xtheories Infinite Xterms and Consistency Problems
Baire Category for Monotone Sets
37 other sections not shown
apply arithmetic assume ATRo Avron axiom of choice axioms bijection binary Boolean algebra bounded cardinal Cohen complete construction Corollary countable critical points definable sets Definition denote dense disjoint Dries elementary embedding elements embeddings equivalent exists extension extensionality fact finite set formula functional interpretation Godel hence hypersequent implies independent induction infinite terms isomorphic Journal of Symbolic Kohlenbach Lambalgen large cardinals Lemma linear logic linearly quantifiable minimal bad monotone monotone functional natural numbers notion o-minimal o-minimal expansion o-minimal structures obtain ordered field ordinals parameters period length Peterzil Pillay predicate functors Presburger Arithmetic Proposition provable prove RCAo real closed field recursive reduction relation relevant logic restricted result satisfies set theory Steinhorn structural rules subalgebra subgroups subset substructural logics Suppose Symbolic Logic tion trivial Troelstra variables zero term zero-one law