June 8, 2024Open Access

Menger and consonant sets in the Sacks model

VHValentin HaberlTU Wien PSPiotr SzewczakCardinal Stefan Wyszyński University in Warsaw LZLyubomyr ZdomskyyTU Wien

Key Points

Key points are not available for this paper at this time.

Abstract

Using an 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 structures of Hurewicz or consonant subsets of the Cantor cube in the Sacks model.

Demander à l'IA

Bookmark

View Full Paper

Cite This Study

Haberl et al. (Sat,) studied this question.

synapsesocial.com/papers/68e65993b6db6435875e883c https://doi.org/https://doi.org/10.48550/arxiv.2406.05457

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1Small Hurewicz and Menger sets which have large continuous images2024
2$Σ^1_3$ sets in the Sacks model2025
3Cantor set, Perfect sets and its Uncountability2026
4The Baire and perfect set properties at singulars cardinals2024
5Schmidt games and Cantor winning sets2024 · 3 citations

Demander à l'IA

Bookmark

View Full Paper