PreprintCC BY-NC-SA 4.0arXiv
Strong failures of club guessing at the successor of a regular cardinal
Abstract
Starting from a model of ZFC, we force the simultaneous failure of the Very Weak Club Guessing and the mho principles at Sκκ+, for any regular cardinal κ. Our results are obtained by means of a forcing iteration technique, due to Krueger, that incorporates models as side conditions. At ω1, the failure of these principles is a well-known consequence of PFA.
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BibTeX
@misc{gallart2026strong,
title = {{Strong failures of club guessing at the successor of a regular cardinal}},
author = {Curial Gallart},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.17547},
eprint = {2608.17547},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.17547},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Strong failures of club guessing at the successor of a regular cardinal
AU - Curial Gallart
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2608.17547
UR - https://arxiv.org/abs/2608.17547
AB - Starting from a model of ZFC, we force the simultaneous failure of the Very Weak Club Guessing and the mho principles at S_κ^κ^+, for any regular cardinal κ. Our results are obtained by means of a forcing iteration technique, due to Krueger, that incorporates models as side conditions. At ω_1, the failure of these principles is a well-known consequence of PFA.
ER -