Of Mice and Machetes

Christopher Henney-Turner; Philip Welch

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arXiv · 2407.21562

Of Mice and Machetes

Christopher Henney-Turner·Philip Welch

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Abstract

Let $R$ be the class of regular cardinals which are not hyperinaccessible. We show that $L[R]$, and similar inner models in the $\alpha$-inaccessible hierarchy, can be generated by iterating a small "machete" mouse up through all the ordinals, and then taking a generic extension by a hyperclass Magidor iteration of Prikry forcings. We then show that such simple mice are themselves elements of $L[\mathsf{Reg}]$.

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Christopher Henney-Turner, Philip Welch. 2024-07-31. Of Mice and Machetes. https://arxiv.org/abs/2407.21562

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