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PreprintCC BY 4.0arXiv

Quadruples and cubes

  • Shimon Garti
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Abstract

We prove, in ZFC, that the λ-terraced cube relation fails whenever λ is an uncountable cardinal. The corresponding terraced relation for quadruples fails for every λ. If λ is ℵ0 then the pretinent terraced relation has consistency strength of at least one Woodin cardinal. We prove positive polarized relations at a successor and a double successor from wondrous ideals. We show, however, that there are no such ideals over two consecutive cardinals simultaneously.

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Cite

BibTeXRIS
BibTeX
@misc{garti2026quadruples,
  title = {{Quadruples and cubes}},
  author = {Shimon Garti},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11239},
  eprint = {2609.11239},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11239},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Quadruples and cubes
AU  - Shimon Garti
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.11239
UR  - https://arxiv.org/abs/2609.11239
AB  - We prove, in ZFC, that the λ-terraced cube relation fails whenever λ is an uncountable cardinal. The corresponding terraced relation for quadruples fails for every λ. If λ is ℵ_0 then the pretinent terraced relation has consistency strength of at least one Woodin cardinal. We prove positive polarized relations at a successor and a double successor from wondrous ideals. We show, however, that there are no such ideals over two consecutive cardinals simultaneously.
ER  -