Elementary equivalence and codimension in p-adic fields.
Elementary equivalence of lattices of open sets definable in o-minimal expansions of real closed fields
We prove that the boolean algebras of sets definable in elementarily equivalent o-minimal expansions of real closed fields are back-and-forth equivalent, and in particular elementarily equivalent, in the language of boolean algebras with new predicates indicating the dimension, Euler characteristic and open sets. We also show that the boolean algebra of semilinear subsets of [0,1]ⁿ definable in an o-minimal expansion of a real closed field is back-and-forth equivalent to the boolean algebra of definable...
Elimination theory for the ring of algebraic integers.
Erblich euklidische Körper.
Errata to the paper "Remarks of the elementary theories of formal and convergent power series" Fundamenta Mathematicae 105 (1980), pp. 229-239
Espace des germes d'arcs réels et série de Poincaré d'un ensemble semi-algébrique
Nous définissons l’espace des germes d’arcs réels tracés sur un ensemble semi-algébrique de , analogue réel de la théorie développée par Denef et Loeser concernant l’espace des germes d’arcs tracés sur une variété algébrique complexe. Puis, reprenant leur méthodes, nous prouvons la rationalité de la série de Poincaré associée à un ensemble semi-algébrique.
Existentially closed domains with radical relations.
Extension of places and contraction properties for function fields over [...]-adically closed fields.
Extensions of Büchi's problem: Questions of decidability for addition and kth powers
We generalize a question of Büchi: Let R be an integral domain, C a subring and k ≥ 2 an integer. Is there an algorithm to decide the solvability in R of any given system of polynomial equations, each of which is linear in the kth powers of the unknowns, with coefficients in C? We state a number-theoretical problem, depending on k, a positive answer to which would imply a negative answer to the question for R = C = ℤ. We reduce a negative answer for k = 2 and for...