The Algebraic nature of the elementary theory of PRC fields.
The Elementary Theory of Algebraic Fields of Finite Corank.
The Elementary Theory of co-Free Ax Fields
The Field of Reals with a Predicate for the Powers of Two.
The limit behaviour of exponential terms
The logic of Rumely's local-global principle.
The model theory of generalized real closed fields.
The prime spectrum of an infinite product of copies of Z
The rationality of the Poincaré series associated to the p-adic points on a variety.
The regular inverse Galois problem over non-large fields
By a celebrated theorem of Harbater and Pop, the regular inverse Galois problem is solvable over any field containing a large field. Using this and the Mordell conjecture for function fields, we construct the first example of a field over which the regular inverse Galois problem can be shown to be solvable, but such that does not contain a large field. The paper is complemented by model-theoretic observations on the diophantine nature of the regular inverse Galois problem.
The Set of Derivatives in a Non-Archimedean Field.
The Undecidability of Pseudo Real Closed Fields.
Théorie des modèles pour des anneaux de fonctions entières et des corps de fonctions méromorphes
Towards a Katona type proof for the 2-intersecting Erdős-Ko-Rado theorem.
Triangulation in o-minimal fields with standard part map
In answering questions of J. Maříková [Fund. Math. 209 (2010)] we prove a triangulation result that is of independent interest. In more detail, let R be an o-minimal field with a proper convex subring V, and let st: V → k be the corresponding standard part map. Under a mild assumption on (R,V) we show that a definable set X ⊆ Vⁿ admits a triangulation that induces a triangulation of its standard part st X ⊆ kⁿ.
Two theorems on regularly r-closed fields.