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112
Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function
 J. Amer. Math. Soc
, 1996
"... Recall that a subset of R n is called semialgebraic if it can be represented as a (finite) boolean combination of sets of the form {�α ∈ R n: p(�α) =0}, {�α ∈R n: q(�α)>0}where p(�x), q(�x) arenvariable polynomials with real coefficients. A map from R n to R m is called semialgebraic if its gr ..."
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Cited by 126 (3 self)
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Recall that a subset of R n is called semialgebraic if it can be represented as a (finite) boolean combination of sets of the form {�α ∈ R n: p(�α) =0}, {�α ∈R n: q(�α)>0}where p(�x), q(�x) arenvariable polynomials with real coefficients. A map from R n to R m is called semialgebraic if its graph, considered
Relational Expressive Power of Constraint Query Languages
"... ... In the course of proving these results for the activedomain semantics, we establish Ramseytype theorems saying that any query involving certain kinds of constraints coincides with a constraintfree query on databases whose elements come from a certain infinite subset of the domain. To prove th ..."
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Cited by 82 (18 self)
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... In the course of proving these results for the activedomain semantics, we establish Ramseytype theorems saying that any query involving certain kinds of constraints coincides with a constraintfree query on databases whose elements come from a certain infinite subset of the domain. To prove the collapse results for the natural semantics, we make use of techniques from nonstandard analysis and from the model theory of ordered structures.
Analytic cell decomposition and analytic motivic integration
 ANN. SCI. ÉCOLE NORM. SUP
, 2006
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