Pablo Cubides Kovacsics

activity

20142026

most citedPro-definability of spaces of definable types

9 citations · 25 across the 14 of their papers we have counts for

collaborators

20 papers

math.LO2026

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…

math.AC2026

Holomorphy rings and the Nullstellensatz over large fields

Pablo Cubides Kovacsics, Sebastián Uribe Rincón

For an infinite field $K$ and an ideal $I \subseteq K [X_{1}, \dots, X_{n}]$ , let $J (Z_{K} (I))$ be the ideal of polynomials vanishing on the $K$ -rational zero locus of $I$ . A Nullstellensatz…

math.LO2026

A Nullstellensatz for the field of complex Laurent series

Pablo Cubides Kovacsics, Sebastián Uribe Rincón

Let $T$ be the theory of the valued field of complex Laurent series $C ((t))$ in the language of rings expanded by a constant for $t$ and by predicates for $n$ -th power…

math.LO2026

Quantifier elimination for lovely pairs of strongly geometric fields

Pablo Cubides Kovacsics, Felipe Estrada, Juan Pérez +1

Let $T$ be a complete strongly geometric theory of fields with quantifier elimination. We show that the theory of lovely pairs of $T$ has quantifier elimination in Delon's definiti…

math.LO2024

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…

math.AC2024

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 $0$ , we show that if one adds another simple condition, t…

math.AG2021

Arc-wise analytic t-stratifications

Pablo Cubides Kovacsics, Immanuel Halupczok

We introduce two new notions of stratifications in valued fields: t $^{2}$ -stratifications and arc-wise analytic t-stratifications. We show the existence of arc-wise analytic t-strati…

math.LO2020★ 1 cited

Definable completeness of $P$ -minimal fields and applications

Pablo Cubides Kovacsics, Françoise Delon

We show that every definable nested family of closed and bounded subsets of a $P$ -minimal field $K$ has non-empty intersection. As an application we answer a question of Darnière a…

math.LO2019

Topological fields with a generic derivation

Pablo Cubides Kovacsics, Françoise Point

We study a class of tame $L$ -theories $T$ of topological fields and their $L_{δ}$ -extension $T_{δ}^{*}$ by a generic derivation $δ$ . The topological fields under cons…

math.LO2019★ 9 cited

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, $p$ -adically…

math.LO2018

Exponential-constructible functions in $P$ -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…

math.LO2017★ 1 cited

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…

math.LO2017

On O-Minimal Expansions of $(Q, <, +, 0)$

Pablo Cubides Kovacsics, Françoise Delon

Let $f : Q \to Q$ be a function definable in an o-minimal expansion of $(Q, <, +, 0)$ . We show that $f$ is eventually linear. In addition, we show that this ho…

math.LO2017★ 2 cited

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,…

math.LO2017★ 1 cited

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…

math.LO2016★ 2 cited

Clustered Cell Decomposition in P-Minimal Structures

Saskia Chambille, Pablo Cubides Kovacsics, Eva Leenknegt

We prove that in a $P$ -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…

math.LO2016★ 4 cited

An example of a $P$ -minimal structure without definable Skolem functions

Pablo Cubides Kovacsics, Kien Huu Nguyen

We show there are intermediate $P$ -minimal structures between the semi-algebraic and sub-analytic languages which do not have definable Skolem functions. As a consequence, by a res…

math.LO2015★ 5 cited

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…

math.LO2015

Integration and Cell Decomposition in $P$ -minimal Structures

Pablo Cubides Kovacsics, Eva Leenknegt

We show that the class of $L$ -constructible functions is closed under integration for any $P$ -minimal expansion of a $p$ -adic field $(K, L)$ . This generalizes re…

math.LO2014

Locally constant functions in C-minimal structures

Pablo Cubides Kovacsics

Let $M$ be a $C$ -minimal structure and $T$ its canonical tree (which corresponds in an ultrametric space to the set of closed balls with radius different than $\infty$ ordered by i…

Analytification and tropicalization via hyperfields and definable types

Holomorphy rings and the Nullstellensatz over large fields

A Nullstellensatz for the field of complex Laurent series

Quantifier elimination for lovely pairs of strongly geometric fields

On residual domination and types orthogonal to the value group

A Characterization of Quasi-homogeneous Bivariate Polynomials

Arc-wise analytic t-stratifications

Definable completeness of P-minimal fields and applications

Topological fields with a generic derivation

Pro-definability of spaces of definable types

Exponential-constructible functions in P-minimal structures

A proof of Liouville's theorem via o-minimality

On O-Minimal Expansions of (Q,<,+,0)

Strong density of definable types and closed ordered differential fields

A note on clustered cells

Clustered Cell Decomposition in P-Minimal Structures

An example of a P-minimal structure without definable Skolem functions

Topological cell decomposition and dimension theory in P-minimal fields

Integration and Cell Decomposition in P-minimal Structures

Locally constant functions in C-minimal structures

Definable completeness of $P$ -minimal fields and applications

Exponential-constructible functions in $P$ -minimal structures

On O-Minimal Expansions of $(Q, <, +, 0)$

An example of a $P$ -minimal structure without definable Skolem functions

Integration and Cell Decomposition in $P$ -minimal Structures