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110
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 128 (4 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
Analytic cell decomposition and analytic motivic integration
 ANN. SCI. ÉCOLE NORM. SUP
, 2006
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Analytic padic cell decomposition and integrals
 Trans. Amer. Math. Soc
"... Abstract. We prove a conjecture of Denef on parameterized padic analytic integrals using an analytic cell decomposition theorem, which we also prove in this paper. This cell decomposition theorem describes piecewise the valuation of analytic functions (and more generally of subanalytic functions), ..."
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Cited by 20 (16 self)
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Abstract. We prove a conjecture of Denef on parameterized padic analytic integrals using an analytic cell decomposition theorem, which we also prove in this paper. This cell decomposition theorem describes piecewise the valuation of analytic functions (and more generally of subanalytic functions), the pieces being geometrically simple sets, called cells. We also classify subanalytic sets up to subanalytic bijection. 1.
Complements of Subanalytic Sets and Existential Formulas for Analytic Functions
 Invent. Math
, 1995
"... We show that the complement of a subanalytic set defined by real analytic functions from any subalgebra closed under differentiation is a subanalytic set defined by the functions from the same subalgebra. This result has an equivalent formulation in logic: Consider an expression built from functions ..."
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Cited by 20 (5 self)
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We show that the complement of a subanalytic set defined by real analytic functions from any subalgebra closed under differentiation is a subanalytic set defined by the functions from the same subalgebra. This result has an equivalent formulation in logic: Consider an expression built from functions as above using equalities and inequalities as well as existential and universal quantifiers. Such an expression is equivalent to an existential expression involving functions from the same class, provided that the variables approach neither infinity nor the boundary of the domain.