  We give a characterizations of toposes which admit a generating family of
objects which are internally cardinal finite (i.e. Kuratowski finite and
decidable) in terms of "topological" conditions. The central result is that,
constructively, a hyperconnected separated locally decidable topos admit a
generating family of cardinal finite objects. The main theorem is then a
generalization obtained as an application of this result internally in the
localic reflection of an arbitrary topos: a topos is generated by cardinal
finite objects if and only if it is separated, locally decidable, and its
localic reflection is zero dimensional.
