We consider definably complete Baire expansions of ordered fields: every definable subset of the domain of the structure has a supremum and the domain cannot be written as the union of a definable… Expand

We prove an effective version of Wilkie's theorem of the complement, so in particular given an expansion of the ordered field R with finitely many C∞ functions, if there are uniform and computable upper bounds on the number of connected components of quantifier free definable sets.Expand

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… Expand

This is an expository paper on a Theorem of the Complement, due to Wilkie, and its generalisations. Wilkie (Sel Math (NS) 5:397–421, 1999) gave necessary and sufficient conditions for an expansion of… Expand

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… Expand

We show how to solve explicitly an equation satisfied by a real function belonging to certain general quasianalytic classes. Examples of the classes under consideration are the collection of… Expand

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.Expand