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 inde-pendent from ZFC. We also analyze the structure of Hurewicz and consonant subsets of the Cantor cube in the Sacks model.
| Original language | English |
|---|---|
| Journal | Journal of Symbolic Logic |
| DOIs | |
| State | Accepted/In press - 2025 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2025 Cambridge University Press. All rights reserved.
Keywords
- Hurewicz property
- Menger property
- Sacks forcing
- consonant
- perfectly meager
- totally imperfect
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