32 citations · 260 across the 75 of their papers we have counts for
15 papers · 1 filter
Universally meager sets in the Miller model and similar ones
Valentin Haberl, Piotr Szewczak, Lyubomyr Zdomskyy
We work in the realm of sets of reals. We prove that in the Miller model and in a model constructed by Goldstern-Judah-Shelah all universally meager sets have size at most . S…
A note on uniform continuity of monotone functions
Roman Pol, Piotr Zakrzewski, Lyubomyr Zdomskyy
We prove that it is consistent with ZFC that for every non-decreasing function , each subset of of cardinality contains a set of cardinality…
Menger and consonant sets in the Sacks model
Valentin Haberl, Piotr Szewczak, Lyubomyr Zdomskyy
Using iterated Sacks forcing and topological games, we prove that the existence of a totally imperfect Menger set in the Cantor cube with cardinality continuum is independent from…
Countably compact extensions and cardinal characteristics of the continuum
Serhii Bardyla, Peter Nyikos, Lyubomyr Zdomskyy
In this paper, we show that the existence of certain first-countable compact-like extensions is equivalent to the equality between corresponding cardinal characteristics of the con…
Coideals as remainders of groups distinguishing between combinatorial covering properties
Giovanni Molica Bisci, Dušan Repovš, Lyubomyr Zdomskyy
In this paper we construct consistent examples of subgroups of with Menger remainders which fail to have other stronger combinatorial covering properties. This answers severa…
On well-splitting posets
Dušan Repovš, Lyubomyr Zdomskyy
We introduce a class of proper posets which is preserved under countable support iterations, includes -bounding, Cohen, Miller, and Mathias posets associated to filters with t…
Convergence of measures after adding a real
Damian Sobota, Lyubomyr Zdomskyy
We prove that if is an infinite Boolean algebra in the ground model and is a notion of forcing adding any of the following reals: a Cohen real, an un…
M-separable spaces of functions are productive in the Miller model
Dušan Repovš, Lyubomyr Zdomskyy
We prove that in the Miller model, every -separable space of the form , where is metrizable and separable, is productively -separable, i.e., is $…
Selection Principles in the Laver, Miller, and Sacks models
Lyubomyr Zdomskyy
This article is devoted to the interplay between forcing with fusion and combinatorial covering properties. We discuss known instances of this interplay as well as present a new on…
Covering properties of -mad families
Leandro Aurichi, Lyubomyr Zdomskyy
We prove that CH implies the existence of a Cohen-indestructible mad family such that the Mathias forcing associated to its filter adds dominating reals, while $\mathfrak b=\mathfr…
Ways of Destruction
Barnabas Farkas, Lyubomyr Zdomskyy
We study the following natural strong variant of destroying Borel ideals: $\textit{$+$-destroys}$ if adds an -positive set whic…
Mathias forcing and combinatorial covering properties of filters
David Chodounský, Dušan Repovš, Lyubomyr Zdomskyy
We give topological characterizations of filters on such that the Mathias forcing adds no dominating reals or preserves ground model unbounded families. This allows u…
Selective covering properties of product spaces, II: gamma spaces
Arnold W. Miller, Boaz Tsaban, Lyubomyr Zdomskyy
We study productive properties of gamma spaces, and their relation to other, classic and modern, selective covering properties. Among other things, we prove the following results:…
On the length of chains of proper subgroups covering a topological group
Taras Banakh, Dušan Repovš, Lyubomyr Zdomskyy
We prove that if an ultrafilter L is not coherent to a Q-point, then each analytic non-sigma-bounded topological group G admits an increasing chain <G_a : a < b(L)> of its proper s…
Combinatorial images of sets of reals and semifilter trichotomy
Boaz Tsaban, Lyubomyr Zdomskyy
Using a dictionary translating a variety of classical and modern covering properties into combinatorial properties of continuous images, we get a simple way to understand the inter…