Frattini Covers and Projective Groups Without the Extension Property.
Fundamental theorems of analysis in formally real fields.
Generalized Archimedean fields and logics with Malitz quantifiers
Idéaux et types sur les corps séparablement clos
Immediate and Purely Wild Extensions of Valued Fields.
Indécidabilité de la théorie des anneaux de séries formelles à plusieurs indéterminées
La théorie d'un anneau de polynômes
Le théorème de MacIntyre sur les ensembles définissables dans les corps -adiques
Levelled O-minimal structures.
We introduce the notion of leveled structure and show that every structure elementarily equivalent to the real expo field expanded by all restricted analytic functions is leveled.
Model theoretic methods in the theory of topological fields.
Model theory of fields: An application to positive semidefinite polynomials
Monomorphisms of inductive number systems
Nice local global fields. IV.
Non standard arithmetic and application to height functions
Non-axiomatizable classes of V-topological fields.
Notes on exponential-logarithmic terms
O-minimal fields with standard part map
Let R be an o-minimal field and V a proper convex subring with residue field k and standard part (residue) map st: V → k. Let be the expansion of k by the standard parts of the definable relations in R. We investigate the definable sets in and conditions on (R,V) which imply o-minimality of . We also show that if R is ω-saturated and V is the convex hull of ℚ in R, then the sets definable in are exactly the standard parts of the sets definable in (R,V).
o-minimality.
On a universal axiomatization of the real closed fields
This paper presents a natural axiomatization of the real closed fields. It is universal and admits quantifier elimination.
On elementary equivalence, isomorphism and isogeny
Motivated by recent work of Florian Pop, we study the connections between three notions of equivalence of function fields: isomorphism, elementary equivalence, and the condition that each of a pair of fields can be embedded in the other, which we call isogeny. Some of our results are purely geometric: we give an isogeny classification of Severi-Brauer varieties and quadric surfaces. These results are applied to deduce new instances of “elementary equivalence implies isomorphism”: for all genus zero...