PreprintarXiv licencearXiv
Short proof that Vopěnka's Principle is symmetrically stable
Abstract
We show that Vopěnka's Principle is stable under symmetric extensions. Recently, de Groot and Woloszyn [1] proved this fact. We found the proof of this theorem unnecessarily complicated. In this short note we prove the same statement. We direct the reader to [3] for an exposition on symmetric extensions.
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BibTeX
@misc{karagila2026short,
title = {{Short proof that Vopěnka's Principle is symmetrically stable}},
author = {Asaf Karagila},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24570},
eprint = {2610.24570},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24570},
}
RIS
TY - UNPB
TI - Short proof that Vopěnka's Principle is symmetrically stable
AU - Asaf Karagila
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.24570
UR - https://arxiv.org/abs/2610.24570
AB - We show that Vopěnka's Principle is stable under symmetric extensions. Recently, de Groot and Woloszyn [1] proved this fact. We found the proof of this theorem unnecessarily complicated. In this short note we prove the same statement. We direct the reader to [3] for an exposition on symmetric extensions.
ER -