A model-theoretic transfer theorem for henselian valued fields.
A remark on Ax's theorem on solvability modulo primes.
A representation of models of Peano arithmetic
Algebraic dimension over Frobenius fields.
Algèbres de Banach ultramétriques, algèbres de Krasner et algèbres de Krasner-Tate
An injective rational map of an abstract algebraic variety into itself.
Analytic cell decomposition and analytic motivic integration
Anelli regolari separabilmente chiusi
Application de la logique à un problème de dimension diophantienne sur les corps
Arithmetic over the rings of all algebraic integers.
Arithmetically independent integers and values of rational functions.
Arithmetization of the field of reals with exponentiation extended abstract
(1) Shepherdson proved that a discrete unitary commutative semi-ring A+ satisfies IE0 (induction scheme restricted to quantifier free formulas) iff A is integral part of a real closed field; and Berarducci asked about extensions of this criterion when exponentiation is added to the language of rings. Let T range over axiom systems for ordered fields with exponentiation; for three values of T we provide a theory in the language of rings plus exponentiation such that the ...
Around Podewski's conjecture
A long-standing conjecture of Podewski states that every minimal field is algebraically closed. Known in positive characteristic, it remains wide open in characteristic zero. We reduce Podewski's conjecture to the (partially) ordered case, and we conjecture that such fields do not exist. We prove the conjecture in case the incomparability relation is transitive (the almost linear case). We also study minimal groups with a (partial) order, and give a complete classification of...
Bounded products in the theory of valued fields.
Bounded statements in the theory of algebraically closed fields with distinguished automophisms.
Cell decomposition for two dimensional local fields
C'est beau et chaud
Clôture algébrique relative de certains anneaux de séries entières
Computing the Galois group of a linear differential equation
Constructing ω-stable structures: Computing rank
This is a sequel to [1]. Here we give careful attention to the difficulties of calculating Morley and U-rank of the infinite rank ω-stable theories constructed by variants of Hrushovski's methods. Sample result: For every k < ω, there is an ω-stable expansion of any algebraically closed field which has Morley rank ω × k. We include a corrected proof of the lemma in [1] establishing that the generic model is ω-saturated in the rank 2 case.