  We introduce an interesting method of proving separable reduction theorems -
the method of elementary submodels. We are studying whether it is true that a
set (function) has given property if and only if it has this property with
respect to a special separable subspace, dependent only on the given set
(function). We are interested in properties of sets "to be dense, nowhere
dense, meager, residual or porous" and in properties of functions "to be
continuous, semicontinuous or Fr\'echet differentiable". Our method of creating
separable subspaces enables us to combine our results, so we easily get
separable reductions of function properties such as "be continuous on a dense
subset", "be Fr\'echet differentiable on a residual subset", etc. Finally, we
show some applications of presented separable reduction theorems and
demonstrate that some results of Zajicek, Lindenstrauss and Preiss hold in
nonseparable setting as well.
