4 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 .…
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…
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…
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…