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 the Katětov order on Borel ideals. We prove two structural theorems (dichotomies),
one for Borel ideals, the other for analytic P-ideals. We isolate nine important Borel ideals …

Say that a class of ultrafilters exists generically if every filter base of size< c can be extended
to an ultrafilter in that class. We investigate generic existence of ultrafilters defined in terms …

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 …

We investigate ideals of the form {A⊆ ω: Σn∈ Axn is unconditionally convergent} where (xn)
n∈ ω is a sequence in a Polish group or in a Banach space. If an ideal on ω can be seen in …

We say that an ideal II on ω ω is homogeneous, if its restriction to any I I-positive subset of ω
ω is isomorphic to I I. The paper investigates basic properties of this notion—we give …

We prove that it is relatively consistent with $\mathsf {ZFC} $ that every maximal ideal is
Katětov above of all $ F_\sigma $ ideals. In particular, we prove that it is consistent that there …

WHEN THE KATETOV ORDER IMPLIES THAT ONE IDEAL EXTENDS THE OTHER? 1.
Introduction Given two ideals I and J we write I ≤ KJ if Page 1 WHEN THE KATETOV ORDER …

Abstract Following Baumgartner (1995)[4], for an ideal I on ω, we say that an ultrafilter U on
ω is an I-ultrafilter if for every function f: ω→ ω there is A∈ U with f [A]∈ I. If there is an I …

For many years, there have been conducting research (eg, by Bergelson, Furstenberg,
Kojman, Kubiś, Shelah, Szeptycki, Weiss) into sequentially compact spaces that are, in a …