5 citations · 10 across the 9 of their papers we have counts for
11 papers
Exponential-constructible functions in -minimal structures
Saskia Chambille, Pablo Cubides Kovacsics, Eva Leenknegt
Exponential-constructible functions are an extension of the class of constructible functions. This extension was formulated by Cluckers-Loeser in the context of semi-algebraic and…
A note on clustered cells
Saskia Chambille, Pablo Cubides Kovacsics, Eva Leenknegt
This note contains additions to the paper 'Clustered cell decomposition in P-minimal structures' (arXiv:1612.02683). We discuss a question which was raised in that paper, on the or…
Clustered Cell Decomposition in P-Minimal Structures
Saskia Chambille, Pablo Cubides Kovacsics, Eva Leenknegt
We prove that in a -minimal structure, every definable set can be partitioned as a finite union of classical cells and regular clustered cells. This is a generalization of previ…
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…
Integration and Cell Decomposition in -minimal Structures
Pablo Cubides Kovacsics, Eva Leenknegt
We show that the class of -constructible functions is closed under integration for any -minimal expansion of a -adic field . This generalizes re…
Uniformly defining valuation rings in Henselian valued fields with finite or pseudo-finite residue fields
Raf Cluckers, Jamshid Derakhshan, Eva Leenknegt +1
We give a definition, in the ring language, of Z_p inside Q_p and of F_p[[t]] inside F_p((t)), which works uniformly for all and all finite field extensions of these fields, an…
Differentiation in P-minimal structures and a p-adic Local Monotonicity Theorem
Tristan Kuijpers, Eva Leenknegt
We prove a p-adic, local version of the Monotonicity Theorem for P-minimal structures. The existence of such a theorem was originally conjectured by Haskell and Macpherson. We appr…
Cell Decomposition for semibounded p-adic sets
Eva Leenknegt
We study a reduct L\ast of the ring language where multiplication is restricted to a neighbourhood of zero. The language is chosen such that for p-adically closed fields K, the L\a…
Cell decomposition and definable functions for weak p-adic structures
Eva Leenknegt
We develop a notion of cell decomposition suitable for studying weak p- adic structures (reducts of p-adic fields where addition and multiplication are not (everywhere) definable).…
Cell decomposition for semi-affine structures on p-adic fields
Eva Leenknegt
We use cell decomposition techniques to study additive reducts of p- adic fields. We consider a very general class of fields, including fields with infinite residue fields, which w…
Parametric rectilinearization for p-adic semi-algebraic sets and rationality of p-adic integrals
Eva Leenknegt
We present a rectilinearization theorem for p-adic semi-algebraic sets depending on parameters. As an application of our main theorem we present an alternative proof of a rationali…