On -categorical theories of fields
p-adic semi-algebraic sets and cell decomposition.
Positively prime models over a normal basic set.
Problemi di decidibilità in logica topologica
Quantifier elimination for modules.
Quantifier elimination in quasianalytic structures via non-standard analysis
The paper is a continuation of an earlier one where we developed a theory of active and non-active infinitesimals and intended to establish quantifier elimination in quasianalytic structures. That article, however, did not attain full generality, which refers to one of its results, namely the theorem on an active infinitesimal, playing an essential role in our non-standard analysis. The general case was covered in our subsequent preprint, which constitutes a basis for the approach presented here....
Quantifier elimination, valuation property and preparation theorem in quasianalytic geometry via transformation to normal crossings
This paper investigates the geometry of the expansion of the real field ℝ by restricted quasianalytic functions. The main purpose is to establish quantifier elimination, description of definable functions by terms, the valuation property and preparation theorem (in the sense of Parusiński-Lion-Rolin). To this end, we study non-standard models of the universal diagram T of in the language ℒ augmented by the names of rational powers. Our approach makes no appeal to the Weierstrass preparation...
Quotients of Semi-Algebraic Spaces.
Rectilinearization of functions definable by a Weierstrass system and its applications
This paper presents several theorems on the rectilinearization of functions definable by a convergent Weierstrass system, as well as their applications to decomposition into special cubes and quantifier elimination.
Résolution du problème de l'ellipse et du cercle par l'algorithme de Hörmander
Rigid subanalytic sets
Sentences with three quantifiers are decidable in set theory
Separably Real Closed Local Rings.
Some (non-)elimination results for curves in geometric structures
We show that the first order structure whose underlying universe is ℂ and whose basic relations are all algebraic subsets of ℂ² does not have quantifier elimination. Since an algebraic subset of ℂ² is either of dimension ≤ 1 or has a complement of dimension ≤ 1, one can restate the former result as a failure of quantifier elimination for planar complex algebraic curves. We then prove that removing the planarity hypothesis suffices to recover quantifier elimination: the structure with the universe...
Sur la complexité du principe de Tarski-Seidenberg
Sur la complexité du principe de Tarski-Seidenberg
The elementary theory of Abelian groups with m-chains of pure subgroups
The Field of Reals with a Predicate for the Powers of Two.
The logic of Rumely's local-global principle.
The rational field is not universally definable in pseudo-exponentiation
We show that the field of rational numbers is not definable by a universal formula in Zilber's pseudo-exponential field.