Of Mice and Machetes

Abstract

Let $R$ be the class of regular cardinals which are not hyperinaccessible. We show that $L[R]$, and similar inner models in the $\hat{I}\pm$-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 $L[\mathsf{Reg}]$.

21 pages