Wilkie (1999) proved a “theorem of the complement” which implies that in order to establish the o-minimality of an expansion of R with C∞ functions it suffices to obtain uniform (in the parameters)… (More)

We show that the theory of the real field with a generic real power function is decidable, relative to an oracle for the rational cut of the exponent of the power function. We show the existence of… (More)

We prove that the zero-set of a C∞ function belonging to a noetherian differential ring M can be written as a finite union of C∞ manifolds which are definable by functions from the same ring. These… (More)

We consider definably complete and Baire expansions of ordered fields: every definable subset of the domain of the structure has a supremum and the domain can not be written as the union of a… (More)