  Assume ZF + AD + $V=L(\mathbb{R})$. We prove some "mouse set" theorems, for
definability over $J_\alpha(\mathbb{R})$ where $[\alpha,\alpha]$ is a
projective-like gap (of $L(\mathbb{R})$) and $\alpha$ is either a successor
ordinal or has countable cofinality, but $\alpha\neq\beta+1$ where $\beta$ ends
a strong gap. For such ordinals $\alpha$ and integers $n\geq 1$, we show that
there is a mouse $M$ with $\mathbb{R}\cap M=\mathrm{OD}_{\alpha n}$.
  The proof involves an analysis of ladder mice and their generalizations to
$J_\alpha(\mathbb{R})$. This analysis is related to earlier work of Rudominer,
Woodin and Steel on ladder mice. However, it also yields a new proof of the
mouse set theorem even at the least point where ladder mice arise -- one which
avoids the stationary tower. The analysis also yields a corresponding
"anti-correctness" result on a cone, generalizing facts familiar in the
projective hierarchy; for example, that $(\Pi^1_3)^V\upharpoonright M_1$ truth
is $(\Sigma^1_3)^{M_1}$-definable and $(\Sigma^1_3)^{M_1}$ truth is
$(\Pi^1_3)^V\upharpoonright M_1$-definable.
  We also define and study versions of ladder mice on a cone at the end of weak
gap, and at the successor of the end of a strong gap, and an anti-correctness
result on a cone there.
