arXiv subjects
Publications and source records attributed to Christopher Henney-Turner.
Let $R$ be the class of regular cardinals which are not hyperinaccessible. We show that $L[R]$, and similar inner models in the $α$-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 $L[\mathsf{Reg}]$.
We introduce two schemes of quantifiers analogous to $I$ and $Q^\text{e.c.}$, which tell us about regular cardinals of small Cantor-Bendixson rank. We examine how the Löwenheim-Skolem-Tarski numbers of these quantifiers interact with one another, and with those of $I$ and $Q^{\text{e.c.}}$. We then find the exact lower bound for each of the LST numbers, assuming the consistency of supercompacts.