Diamonds in mice
Year: 2026
Type: preprint
Abstract: Let $M$ be a $(0,ω_1+1)$-iterable mouse with no largest cardinal. Let $γ\leqκ$ 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 $κ\geqω_1^M$ be a cardinal of $M$. Then $M$ satisfies $\diamondsuit^*_{κω_1^M}$.
Source: arXiv (Cornell University)
Author: Schlutzenberg, Farmer
Institution: TU Wien
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213312351
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