Menger and consonant sets in the Sacks model

2024/06/08 by Valentin Haberl, Haberl, Valentin, Piotr Szewczak +3
Computer Science · #03E35 #54A35 #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2406.05457

openalex publication_date 2024/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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