MENGER and CONSONANT SETS in the SACKS MODEL

Valentin Haberl; P. I.O.T.R. Szewczak; Lyubomyr Zdomskyy

doi:10.1017/jsl.2025.21

MENGER and CONSONANT SETS in the SACKS MODEL

Valentin Haberl, P. I.O.T.R. Szewczak, Lyubomyr Zdomskyy

Research output: Contribution to journal › Article › peer-review

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	https://doi.org/10.1017/jsl.2025.21
State	Accepted/In press - 2025
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2025 Cambridge University Press. All rights reserved.

Keywords

consonant
Hurewicz property
Menger property
perfectly meager
Sacks forcing
totally imperfect

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10.1017/jsl.2025.21

Cite this

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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.",

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MENGER and CONSONANT SETS in the SACKS MODEL

Abstract

Bibliographical note

Keywords

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