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math.GN2024
Small Hurewicz and Menger sets which have large continuous images
Piotr Szewczak, Tomasz Weiss, Lyubomyr Zdomskyy
We provide new techniques to construct sets of reals without perfect subsets and with the Hurewicz or Menger covering properties. In particular, we show that if the Continuum Hypot…
math.LO2024
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…