22 citations · 105 across the 33 of their papers we have counts for
13 papers · 1 filter
Two or not two ?
Rafał Filipów, Adam Kwela
The paper is devoted to comparison of two generalizations of the bounding number .
More on yet another ideal version of the bounding number
Adam Kwela
This is a continuation of the paper [J. Symb. Log. 87 (2022), 1065--1092]. For an ideal on we denote $\mathcal{D}_{\mathcal{I}}=\{f\inω^ω: f^{-1}[\{n\}]\in\mathca…
Egorov ideals
Adam Kwela
We study Egorov ideals, that is ideals on for which the Egorov's theorem for ideal versions of pointwise and uniform convergences holds. We show that a non-pathological $\bf{Σ^…
Characterizing existence of certain ultrafilters
Rafał Filipów, Krzysztof Kowitz, Adam Kwela
Following Baumgartner [J. Symb. Log. 60 (1995), no. 2], for an ideal on , we say that an ultrafilter on is an -ultrafilter if for ev…
Yet another ideal version of the bounding number
Rafał Filipów, Adam Kwela
Let be an ideal on . For we write if for all with some . Moreover, we den…
Katětov order between Hindman, Ramsey, van der Waerden and summable ideals
Rafał Filipów, Krzysztof Kowitz, Adam Kwela
A family I of subsets of a set X is an ideal on X if it is closed under taking subsets and finite unions of its elements. An ideal I on X is below an ideal J on Y in the Katetov or…
On a conjecture of Debs and Saint Raymond
Adam Kwela
Borel separation rank of an analytic ideal on is the minimal ordinal such that there is with $\mathcal{I}\subseteq \mathc…
On extendability to ideals
Adam Kwela
Answering in negative a question of M. Hrušák, we construct a Borel ideal not extendable to any ideal and such that it is not Katětov above the ideal .
Inductive limits of ideals
Adam Kwela
G. Debs and J. Saint Raymond in 2009 defined the Borel separation rank of an analytic ideal () as minimal ordinal such that there is…
Homogeneous ideals on countable sets
Adam Kwela, Jacek Tryba
We say that an ideal I is homogeneous, if its restriction to any I-positive subset is isomorphic to I. The paper investigates basic properties of this notion -- we give examples of…
Additivity of the ideal of microscopic sets
Adam Kwela
A set is microscopic if for each there is a sequence of intervals covering and such that for…
Ranks of -limits of filter sequences
Adam Kwela, Ireneusz Recław
We give an exact value of the rank of an -Fubini sum of filters for the case where is a Borel filter of rank . We also consider -limits o…
Topological representations
Adam Kwela, Marcin Sabok
This paper studies the combinatorics of ideals which recently appeared in ergodicity results for analytic equivalence relations. The ideals have the following topological represent…