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PreprintarXiv licencearXiv

A non-trivially non-trivial automorphism at an inaccessible cardinal

  • Márk Poór
  • Jing Zhang
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Abstract

We show that, relative to the existence of an inaccessible cardinal, it is consistent that for an inaccessible cardinal κ, there is a non-trivial automorphism of 𝒫(κ)/fin whose restriction to 𝒫(β)/fin is induced by a bijection on β for every β<κ. This answers questions posed by Larson--McKenney, Shelah--Steprāns, and Veličković.

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Cite

BibTeXRIS
BibTeX
@misc{poor2026nontrivially,
  title = {{A non-trivially non-trivial automorphism at an inaccessible cardinal}},
  author = {Márk Poór and Jing Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08061},
  eprint = {2609.08061},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08061},
}
RIS
TY  - UNPB
TI  - A non-trivially non-trivial automorphism at an inaccessible cardinal
AU  - Márk Poór
AU  - Jing Zhang
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.08061
UR  - https://arxiv.org/abs/2609.08061
AB  - We show that, relative to the existence of an inaccessible cardinal, it is consistent that for an inaccessible cardinal κ, there is a non-trivial automorphism of 𝒫(κ)/fin whose restriction to 𝒫(β)/fin is induced by a bijection on β for every β<κ. This answers questions posed by Larson--McKenney, Shelah--Steprāns, and Veličković.
ER  -