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math.LO2025
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…
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…