6 citations · 20 across the 9 of their papers we have counts for
11 papers
Defining integer valued functions in rings of continuous definable functions over a topological field
Luck Darnière, Marcus Tressl
Let K be an expansion of either an ordered field or a valued field. Given a definable set X K<sup>m</sup> let C(X) be the ring of continuous definable functions from X…
On the model-completion of Heyting algebras
Luck Darnière
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 introduc…
Model completion of scaled lattices and co-Heyting algebras of p-adic semi-algebraic sets
Luck Darnière
Let p be prime number, K be a p-adically closed field, X K^m a semi-algebraic set defined over K and L(X) the lattice of semi-algebraic subsets of X which are closed in…
Semi-algebraic triangulation over p-adically closed fields
Luck Darnière
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 exis…
Polytopes and simplexes in p-adic fields
Luck Darnière
We introduce topological notions of polytopes and simplexes, the latter being expected to play in p-adically closed fields the role played by real simplexes in the classical result…
Topological cell decomposition and dimension theory in P-minimal fields
Pablo Cubides-Kovacsics, Luck Darnière, Eva Leenknegt
This paper addresses some questions about dimension theory for P-minimal structures. We show that, for any definable set A, the dimension of the frontier of A is strictly smaller t…