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PreprintCC BY 4.0arXiv

Fragments of SRP, the nonstationary ideal, and diagonal reflection

  • Gunter Fuchs
  • Hiroshi Sakai
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Abstract

We investigate the relationships between fragments of SRP and diagonal reflection principles. It turns out that the subcomplete fragment of SRP, augmented with CH, implies that the nonstationary ideal on ω1 is not saturated, but that Larson's diagonal reflection principle OSRω2 holds. In contrast, it was known that the full principle SRP implies the saturation of the nonstationary ideal on ω1, but it does not imply OSRω2. We find several instances of this phenomenon: pairing (variations of) the subcomplete fragment of SRP with stronger failures of the nonstationary ideal on ω1 to be saturated allows us to conclude more instances of diagonal reflection principles, while boosting (the corresponding variations of) the full principle SRP with strong forms of the saturation of the nonstationary ideal allows us to produce models where these principles still hold, yet weaker versions of diagonal reflection fail.

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Cite

BibTeXRIS
BibTeX
@misc{fuchs2026fragments,
  title = {{Fragments of SRP, the nonstationary ideal, and diagonal reflection}},
  author = {Gunter Fuchs and Hiroshi Sakai},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.17547},
  eprint = {2610.17547},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.17547},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Fragments of SRP, the nonstationary ideal, and diagonal reflection
AU  - Gunter Fuchs
AU  - Hiroshi Sakai
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.17547
UR  - https://arxiv.org/abs/2610.17547
AB  - We investigate the relationships between fragments of SRP and diagonal reflection principles. It turns out that the subcomplete fragment of SRP, augmented with CH, implies that the nonstationary ideal on ω_1 is not saturated, but that Larson's diagonal reflection principle OSR_ω_2 holds. In contrast, it was known that the full principle SRP implies the saturation of the nonstationary ideal on ω_1, but it does not imply OSR_ω_2. We find several instances of this phenomenon: pairing (variations of) the subcomplete fragment of SRP with stronger failures of the nonstationary ideal on ω_1 to be saturated allows us to conclude more instances of diagonal reflection principles, while boosting (the corresponding variations of) the full principle SRP with strong forms of the saturation of the nonstationary ideal allows us to produce models where these principles still hold, yet weaker versions of diagonal reflection fail.
ER  -