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Quantifier Elimination in SecondOrder Predicate Logic
, 1992
"... An algorithm is presented which eliminates secondorder quantiers over predicate variables in formulae of type 9P 1 ; . . . ; Pn where is an arbitrary formula of firstorder predicate logic. The resulting formula is equivalent to the original formula  if the algorithm terminates. The algorithm ..."
Abstract

Cited by 56 (5 self)
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An algorithm is presented which eliminates secondorder quantiers over predicate variables in formulae of type 9P 1 ; . . . ; Pn where is an arbitrary formula of firstorder predicate logic. The resulting formula is equivalent to the original formula  if the algorithm terminates. The algorithm can for example be applied to do interpolation, to eliminate the secondorder quantiers in circumscription, to compute the correlations between structures and power structures, to compute semantic properties corresponding to Hilbert axioms in non classical logics and to compute model theoretic semantics for new logics. An earlier version of the paper has been published in [GO92b].
Elimination of Predicate Quantifiers
 UWE REYLE, HANS JÜRGEN OHLBACH (EDS.): LOGIC, LANGUAGE AND REASONING  ESSAYS IN HONOUR OF DOV GABBAY
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Hilbert’s twentyfourth problem
 American Mathematical Monthly
, 2001
"... 1. INTRODUCTION. For geometers, Hilbert’s influential work on the foundations of geometry is important. For analysts, Hilbert’s theory of integral equations is just as important. But the address “Mathematische Probleme ” [37] that David Hilbert (1862– 1943) delivered at the second International Cong ..."
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Cited by 10 (4 self)
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1. INTRODUCTION. For geometers, Hilbert’s influential work on the foundations of geometry is important. For analysts, Hilbert’s theory of integral equations is just as important. But the address “Mathematische Probleme ” [37] that David Hilbert (1862– 1943) delivered at the second International Congress of Mathematicians (ICM) in Paris has tremendous importance for all mathematicians. Moreover, a substantial part of