4 papers
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…
Concentrated sets and the Hurewicz property
Valentin Haberl, Piotr Szewczak, Lyubomyr Zdomskyy
A set of reals is -concentrated if it has cardinality at least and it contains a countable set such that each closed subset of d…
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…
Concentrated sets and -sets in the Miller model
Valentin Haberl, Piotr Szewczak, Lyubomyr Zdomskyy
Using combinatorial covering properties, we show that there is no concentrated set of reals of size in the Miller model. The main result refutes a conjecture of Bartoszyński…