On the real exponential field with restricted analytic functions
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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