MENGER AND CONSONANT SETS IN THE SACKS MODEL
Valentin Haberl, Piotr Szewczak, Lyubomyr Zdomskyy · Journal of Symbolic Logic · 2025
Abstract 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 ZFC. We also analyze the structure of Hurewicz and consonant subsets of the Cantor cube in the Sacks model.