Translation procedures in descriptive inner model theory

Abstract

We develop a basic translation procedure that translates a hod mouse to an equivalent mouse. Unlike the translation procedure used by Steel and Zhu, our procedure works in a coarse setting without assuming AD. Nevertheless, the procedure resembles the one developed by Steel. We use the translation procedures to answer a question of Trevor Wilson. Namely, we show that if there is a stationary class of lambda such that lambda is a limit of Woodin cardinals and the derived model at lambda satisfies AD the first member of the Solovay sequence is is less than Theta then there is a transitive model M such that M contains the ordinals and satisfies there is a proper class of Woodin cardinals and a strong cardinal.