Luck Darnière
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View article: Semi‐algebraic triangulation over p‐adically closed fields
Semi‐algebraic triangulation over p‐adically closed fields Open
We prove a triangulation theorem for semi-algebraic sets over a p-adically\nclosed field, quite similar to its real counterpart. We derive from it several\napplications like the existence of flexible retractions and splitting for\nsemi-alg…
View article: Defining integer valued functions in rings of continuous definable functions over a topological field
Defining integer valued functions in rings of continuous definable functions over a topological field Open
Let K be an expansion of either an ordered field or a valued field. Given a definable set X $\subseteq$ Km let C(X) be the ring of continuous definable functions from X to K. Under very mild assumptions on the geometry of X and on the stru…
View article: On the model-completion of Heyting algebras
On the model-completion of Heyting algebras Open
We axiomatize the model-completion of the theory of Heyting algebras by means of the "Density" and "Splitting" properties in [DJ18], and of a certain "QE Property" that we introduce here. In addition: we prove that this model-completion ha…
View article: Model completion of scaled lattices and co-Heyting algebras of p-adic semi-algebraic sets
Model completion of scaled lattices and co-Heyting algebras of p-adic semi-algebraic sets Open
Let p be prime number, K be a p-adically closed field, X $\subseteq$ K^m a semi-algebraic set defined over K and L(X) the lattice of semi-algebraic subsets of X which are closed in X. We prove that the complete theory of L(X) eliminates th…
View article: Scaled lattices of closed p-adic semi-algebraic sets
Scaled lattices of closed p-adic semi-algebraic sets Open
Let p be prime number, K be a p-adically closed field, X $\subseteq$ K m a semi-algebraic set defined over K and L(X) the lattice of semi-algebraic subsets of X which are closed in X. We prove that the complete theory of L(X) eliminates th…
View article: TOPOLOGICAL CELL DECOMPOSITION AND DIMENSION THEORY IN <i>P</i>-MINIMAL FIELDS
TOPOLOGICAL CELL DECOMPOSITION AND DIMENSION THEORY IN <i>P</i>-MINIMAL FIELDS Open
This paper addresses some questions about dimension theory for P -minimal structures. We show that, for any definable set A, the dimension of $\bar A\backslash A$ is strictly smaller than the dimension of A itself, and that A has a decompo…
View article: Semi-algebraic triangulation over p-adically closed fields
Semi-algebraic triangulation over p-adically closed fields Open
We prove a triangulation theorem for semi-algebraic sets over a p-adically closed field, quite similar to its real counterpart. We derive from it several applications like the existence of flexible retractions and splitting for semi-algebr…