On the real exponential field with restricted analytic functions
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The model-theoretic structure (ℝan, exp) is investigated as a special case of an expansion of the field of reals by certain families ofC ∞-functions. In particular, we use methods of Wilkie to show that (ℝan, exp) is (finitely) model complete and O-minimal. We also prove analytic cell decomposition and the fact that every definable unary function is ultimately bounded by an iterated exponential function.
KeywordsRegular Solution Model Completeness Noetherian Ring Cell Decomposition Divisible Group
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- [vdD-M-M] L. van den Dries, A. Macintyre and D. Marker,The elementary theory of restricted analytic fields with exponentiation, Annals of Mathematics, to appear.Google Scholar
- [H] A. G. Hovanskii,On a class of systems of transcendental equations, Soviet Math. Dokl.22 (1980), 762–765.Google Scholar
- [Re] J.-P. Ressayre,Integer parts of real closed exponential fields, preprint.Google Scholar
- [W1] A. J. Wilkie,Model completeness results for expansions of the real ordered field I: Restricted Pfaffian functions, preprint 1991.Google Scholar
- [W2] A. J. Wilkie,Model completeness results for expansions of the real field II: the exponential function, preprint 1992.Google Scholar