Scales and the fine structure of K(R). Part II: Weak real mice and scales

Abstract

We define weak real mice $\mathcal{M}$ and prove that the boldface pointclass $\boldsymbol{\Sigma}_m(\mathcal{M})$ has the scale property assuming only the determinacy of sets of reals in $\mathcal{M}$ when $m$ is the smallest integer $m>0$ such that $\boldsymbol{\Sigma}_m(\mathcal{M})$ contains a set of reals not in $\mathcal{M}$. We shall use this development in Part III to obtain scales of minimal complexity in $K(\mathbb{R})$.