9 citations · 25 across the 14 of their papers we have counts for
20 papers
Analytification and tropicalization via hyperfields and definable types
Pablo Cubides Kovacsics, Mariana Vicaría, Jinhe Ye
We study the analytification and tropicalization of algebraic varieties over valued fields via Jun's spaces of hyperfield points. Our main new objects are a family of power-tropica…
Holomorphy rings and the Nullstellensatz over large fields
Pablo Cubides Kovacsics, Sebastián Uribe Rincón
For an infinite field and an ideal , let be the ideal of polynomials vanishing on the -rational zero locus of . A Nullstellensatz…
A Nullstellensatz for the field of complex Laurent series
Pablo Cubides Kovacsics, Sebastián Uribe Rincón
Let be the theory of the valued field of complex Laurent series in the language of rings expanded by a constant for and by predicates for -th power…
Quantifier elimination for lovely pairs of strongly geometric fields
Pablo Cubides Kovacsics, Felipe Estrada, Juan Pérez +1
Let be a complete strongly geometric theory of fields with quantifier elimination. We show that the theory of lovely pairs of has quantifier elimination in Delon's definiti…
On residual domination and types orthogonal to the value group
Pablo Cubides Kovacsics, Silvain Rideau-Kikuchi, Mariana Vicaría
We present a unifying framework of residual domination for (expansions of) henselian valued fields of equicharacteristic zero, encompassing some valued fields with operators. We sh…
A Characterization of Quasi-homogeneous Bivariate Polynomials
David Bradley-Williams, Pablo Cubides Kovacsics, Immanuel Halupczok
If a reduced bivariate polynomial is quasi-homogeneous, then its discriminant is a monomial. Over fields of characteristic , we show that if one adds another simple condition, t…
Arc-wise analytic t-stratifications
Pablo Cubides Kovacsics, Immanuel Halupczok
We introduce two new notions of stratifications in valued fields: t-stratifications and arc-wise analytic t-stratifications. We show the existence of arc-wise analytic t-strati…
Definable completeness of -minimal fields and applications
Pablo Cubides Kovacsics, Françoise Delon
We show that every definable nested family of closed and bounded subsets of a -minimal field has non-empty intersection. As an application we answer a question of Darnière a…
Topological fields with a generic derivation
Pablo Cubides Kovacsics, Françoise Point
We study a class of tame -theories of topological fields and their -extension by a generic derivation . The topological fields under cons…
Pro-definability of spaces of definable types
Pablo Cubides Kovacsics, Jinhe Ye
We show pro-definability of spaces of definable types in various classical complete first order theories, including complete o-minimal theories, Presburger arithmetic, -adically…
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 proof of Liouville's theorem via o-minimality
Pablo Cubides Kovacsics
In this short note we give a proof of Liouville's theorem (every bounded entire complex function is constant) following Peterzil and Starchenko's approach to complex analysis via o…
On O-Minimal Expansions of
Pablo Cubides Kovacsics, Françoise Delon
Let be a function definable in an o-minimal expansion of . We show that is eventually linear. In addition, we show that this ho…
Strong density of definable types and closed ordered differential fields
Quentin Brouette, Pablo Cubides Kovacsics, Francoise Point
The following strong form of density of definable types is introduced for theories T admitting a fibered dimension function d: given a model M of T and a definable subset X of M^n,…
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…
An example of a -minimal structure without definable Skolem functions
Pablo Cubides Kovacsics, Kien Huu Nguyen
We show there are intermediate -minimal structures between the semi-algebraic and sub-analytic languages which do not have definable Skolem functions. As a consequence, by a res…
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…
Locally constant functions in C-minimal structures
Pablo Cubides Kovacsics
Let be a -minimal structure and its canonical tree (which corresponds in an ultrametric space to the set of closed balls with radius different than ordered by i…