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A weak λ-set that is not a λ-set under frakp = frakc
Abstract
Under p=c, Cantor space contains a weak λ-set that is not a λ-set. This answers the consistency question of de Oliveira Rodrigues, dos Santos Ronchim, and Szeptycki. The hypothesis p=c is compatible with the failure of the continuum hypothesis. The construction combines the finite-unions form of Hindman's theorem with Bell's characterization of p in terms of σ-centered forcing. The increasing enumerations of the infinite members of the constructed space form an unbounded family under eventual domination. This makes the countable set of finite subsets of ω a witness to the failure of the λ-property.
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BibTeX
@misc{osipov2026weak,
title = {{A weak $λ$-set that is not a $λ$-set under $\frakp = \frakc$}},
author = {Alexander V. Osipov and Anton E. Lipin},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06312},
eprint = {2611.06312},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06312},
}
RIS
TY - UNPB
TI - A weak λ-set that is not a λ-set under frakp = frakc
AU - Alexander V. Osipov
AU - Anton E. Lipin
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06312
UR - https://arxiv.org/abs/2611.06312
AB - Under p=c, Cantor space contains a weak λ-set that is not a λ-set. This answers the consistency question of de Oliveira Rodrigues, dos Santos Ronchim, and Szeptycki. The hypothesis p=c is compatible with the failure of the continuum hypothesis. The construction combines the finite-unions form of Hindman's theorem with Bell's characterization of p in terms of σ-centered forcing. The increasing enumerations of the infinite members of the constructed space form an unbounded family under eventual domination. This makes the countable set of finite subsets of ω a witness to the failure of the λ-property.
ER -