A general model completeness result for expansions of the real ordered field Original Research Article

We approach the subject of o-minimality from the point of view of tame systems, following the work of Charbonnel and Wilkie. This gives some general sufficient conditions for a system to be model complete and o-minimal. We are then able to obtain the following generalisation of a recent result of Gabrielov (which in his case applied only to analytic functions): A polynomially bounded o-minimal expansion of the real ordered field by a collection of restricted C∝ functions, which is closed under partial differentiation, is model complete.