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.Sections 9-14. Some partial results on capturing Σ 2 1 truths in AD + models by mice. (That is, partial results on the mouse set conjecture.)Section 15 A theorem of Woodin on the consistency strength of AD + + θ 0 < θ.
Section 16The global mouse set conjecture implies its local version.Section 17 Capturing sets of reals in R-mice.