Comparison of fine structural mice via coarse iteration

Abstract

Let \({\mathcal{M}}\) be a fine structural mouse. Let \({\mathbb{D}}\) be a fully backgrounded \({L[\mathbb{E}]}\)-construction computed inside an iterable coarse premouse S. We describe a process comparing \({\mathcal{M}}\) with \({\mathbb{D}}\), through forming iteration trees on \({\mathcal{M}}\) and on S. We then prove that this process succeeds.