Disjoint Stationary Sequences on an Interval of Cardinals

Hannes Jakob

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arXiv · 2309.01986

Disjoint Stationary Sequences on an Interval of Cardinals

Hannes Jakob

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Abstract

We answer a question of Krueger by obtaining -- from countably many Mahlo cardinals -- a model where there is a disjoint stationary sequence on $\aleph_{n+2}$ for every $n\in\omega$. In that same model, the notions of being internally stationary and internally club are distinct on a stationary subset of $[H(\Theta)]^{\aleph_{n+1}}$ for every $n\in\omega$ and $\Theta\geq\aleph_{n+2}$, answering another of Krueger's questions. This is obtained by employing a product of variants of Mitchell forcing which uses finite support for the Cohen reals and full support for the countably many collapses.

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BibTeX RIS

Hannes Jakob. 2023-09-05. Disjoint Stationary Sequences on an Interval of Cardinals. https://arxiv.org/abs/2309.01986

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