MENGER AND CONSONANT SETS IN THE SACKS MODEL
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.
Authors
- Lyubomyr Zdomskyy (ORCID: https://orcid.org/0000-0002-7450-2420)
- Piotr Szewczak (ORCID: https://orcid.org/0000-0001-7961-7748)
- Valentin Haberl (ORCID: https://orcid.org/0009-0007-8237-7811)
Institutions
- TU Wien (AT)
- Cardinal Stefan Wyszynski University in Warsaw (PL)
Publication Details
- Journal
- Journal of Symbolic Logic
- Published
- 2025-03-06
- DOI
- https://doi.org/10.1017/jsl.2025.21
- Primary Topic
- Cellular Automata and Applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Austrian Science Fund