  A "numerical set-expression" is a term specifying a cascade of arithmetic and
logical operations to be performed on sets of non-negative integers. If these
operations are confined to the usual Boolean operations together with the
result of lifting addition to the level of sets, we speak of "additive
circuits". If they are confined to the usual Boolean operations together with
the result of lifting addition and multiplication to the level of sets, we
speak of "arithmetic circuits". In this paper, we investigate the definability
of sets and functions by means of additive and arithmetic circuits,
occasionally augmented with additional operations.
