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 …

This book is shorter than In Search of Lost Time, is easier to read than Principia
Mathematica, and has more mathematical content than War and Peace. 1, 2 It provides an …

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 …

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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 …

This is a ``preproof'' accepted article for The Journal of Symbolic Logic. This version may be
subject to change during the prod Page 1 LEBESGUE MEASURE ZERO MODULO IDEALS ON …

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 …

The~\emph {Rothberger number} $\mathfrak {b}(\mathcal {I}) $ of a definable ideal $\mathcal
{I} $ on $\omega $ is the least cardinal $\kappa $ such that there exists a Rothberger gap of …

We continue to investigate the notion of IK-convergence (which concerns with the
convergence with respect to one ideal along a set which is “big” with respect to another …