Full normalization for $\kappa^+$-supercompactness

TL;DR

This paper extends normalization results to mice at the level of + supercompactness, showing how to extend strategies for stacks of trees while preserving normality and condensation properties.

Contribution

It introduces a method to extend normal iteration strategies for + supercompact mice to stacks, maintaining key properties and generalizing previous normalization results.

Findings

Extension of strategies preserves normality.

Strategies satisfy condensation properties.

Normal iterates are preserved under extension.

Abstract

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