  A pointwise definable model is one in which every object is definable without
parameters. In a model of set theory, this property strengthens V=HOD, but is
not first-order expressible. Nevertheless, if ZFC is consistent, then there are
continuum many pointwise definable models of ZFC. If there is a transitive
model of ZFC, then there are continuum many pointwise definable transitive
models of ZFC. What is more, every countable model of ZFC has a class forcing
extension that is pointwise definable. Indeed, for the main contribution of
this article, every countable model of Godel-Bernays set theory has a pointwise
definable extension, in which every set and class is first-order definable
without parameters.
