Recall that M_1 is the minimal proper class mouse with a Woodin cardinal δ. We will consider models of the form M_1[Σ], where Σ is a fragment of the iteration strategy for M_1. In particular, we will discuss how much strategy Σ can be added without destroying the Woodinness of δ. We will also discuss the κ-mantle of M_1, for certain values of κ.
Keywords: Set theory; inner model theory; strategy mouse; set theoretic geology