  This paper classifies the complexity of various teaching models by their
position in the arithmetical hierarchy. In particular, we determine the
arithmetical complexity of the index sets of the following classes: (1) the
class of uniformly r.e. families with finite teaching dimension, and (2) the
class of uniformly r.e. families with finite positive recursive teaching
dimension witnessed by a uniformly r.e. teaching sequence. We also derive the
arithmetical complexity of several other decision problems in teaching, such as
the problem of deciding, given an effective coding $\{\mathcal L_0,\mathcal
L_1,\mathcal L_2,\ldots\}$ of all uniformly r.e. families, any $e$ such that
$\mathcal L_e = \{L^e_0,L^e_1,\ldots,\}$, any $i$ and $d$, whether or not the
teaching dimension of $L^e_i$ with respect to $\mathcal L_e$ is upper bounded
by $d$.
