# Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function

@article{Wilkie1996ModelCR, title={Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function}, author={A. J. Wilkie}, journal={Journal of the American Mathematical Society}, year={1996}, volume={9}, pages={1051-1094} }

Recall that a subset of R is called semi-algebraic if it can be represented as a (finite) boolean combination of sets of the form {~ α ∈ R : p(~ α) = 0}, {~ α ∈ R : q(~ α) > 0} where p(~x), q(~x) are n-variable polynomials with real coefficients. A map from R to R is called semi-algebraic if its graph, considered as a subset of R, is so. The geometry of such sets and maps (“semi-algebraic geometry”) is now a widely studied and flourishing subject that owes much to the foundational work in the… Expand

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