Diamonds in mice — Draconitic Research

Abstract

Let M be a (0,ω₁+1)-iterable mouse with no largest cardinal. Let γ≤κ be uncountable cardinals of M, with κ regular in M. Then M satisfies diamondsuit_κγ⁺, and if κ is non-ineffable in M then M satisfies diamondsuit_κκ⁺. Suppose that either ω₁^M=ω₁ or M satisfies "I am (0,ω₁+1)-iterable". Let κ≥ω₁^M be a cardinal of M. Then M satisfies diamondsuit^*_κω₁^M.

Cite

BibTeX RIS

BibTeX

@misc{schlutzenberg2026diamonds,
  title = {{Diamonds in mice}},
  author = {Farmer Schlutzenberg},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13934},
  eprint = {2609.13934},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13934},
}

RIS

TY  - UNPB
TI  - Diamonds in mice
AU  - Farmer Schlutzenberg
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2609.13934
UR  - https://arxiv.org/abs/2609.13934
AB  - Let M be a (0,ω_1+1)-iterable mouse with no largest cardinal. Let γ≤κ be uncountable cardinals of M, with κ regular in M. Then M satisfies diamondsuit_κγ^+, and if κ is non-ineffable in M then M satisfies diamondsuit_κκ^+. Suppose that either ω_1^M=ω_1 or M satisfies "I am (0,ω_1+1)-iterable". Let κ≥ω_1^M be a cardinal of M. Then M satisfies diamondsuit^*_κω_1^M.
ER  -