Full normalization for $\hat{I}{º}^{+}$-supercompactness

Abstract

We extend the normalization results of the author's paper "Full normalization for transfinite stacks" [5] to mice at the level of $\hat{I}{º}^{+}$-supercompactness: given a normal iteration strategy $\hat{I}\pounds$ for such a mouse $M$, with both $M$ and $\hat{I}\pounds$ satisfying certain condensation properties, we extend $\hat{I}\pounds$ to a strategy $\hat{I}{\pounds }^{\ast }$ for stacks of normal trees, such that every iterate via $\hat{I}{\pounds }^{\ast }$ is in fact a normal iterate via $\hat{I}\pounds$.

24 pages