DERIVED MODELS ASSOCIATED TO MICE

Abstract

We shall present some results on the the properties of derived models of mice, and on the existence of mice with large derived models. The basic plan of the paper is: Sections 1–5. Introduction. Preliminary definitions and background material. The iteration independence of the derived model associated to a mouse. The mouse set conjecture in derived models associated to mice. Sections 6–8 The Solovay sequence in derived models associated to mice. A method of “translating away ” extenders overlapping Woodin cardinals in mice.