An ideal on a set X is a collection of subsets of X closed under the operations of taking finite
unions and subsets of its elements. Ideals are a very useful notion in topology and set theory …

We study several combinatorial properties of (mostly definable) ideals on countable sets. In
several cases, we identify critical ideals for such properties in the Katětov order. In particular …

Let $ X $ be an uncountable Polish space and let $\mathcal {I} $ be an ideal on $\omega $.
A point $\eta\in X $ is an $\mathcal {I} $-limit point of a sequence $(x_n) $ taking values in …

If F is a filter on ω, we say that F is Canjar if the corresponding Mathias forcing does not add
a dominating real. We prove that any Borel Canjar filter is F σ, solving a problem of Hrušák …

Given an ideal $\mathcal {I} $ on the nonnegative integers $\omega $ and a Polish space $
X $, let $\mathscr {L}(\mathcal {I}) $ be the family of subsets $ S\subseteq X $ such that $ S …

In this paper we mainly study the Borel complexity of ideal limit points, denoted by Λ r (I), in a
first countable space. We investigate the connection between complexity of Λ r (I) and …

We study $\mathcal I $-maximal eventually different families of functions from the set of
natural numbers into itself where $\mathcal I $ is an arbitrary ideal on the set of natural …

We prove, without any form of determinacy, that $ F_\sigma $ filters are exactly filters
$\omega $-diagonalizable by $\mathcal F^+ $-universal sets. For analytic filters, $ F_\sigma …

If F is a filter on ω, we say that F is Canjar if the corresponding Mathias forcing does not add
a dominating real. We prove that any Borel Canjar filter is Fσ, this solves a problem of …

En esta tesis se usan métodos de la combinatoria infinita para estudiar problemas de la
teoría de conjuntos y topología. En particular, se estudian los temas de ideales Canjar …