  The monadic second-order theory of trees allows quantification over elements
and over arbitrary subsets. We classify the class of trees with respect to the
question: does a tree T have definable Skolem functions (by a monadic formula
with parameters)? This continues [LiSh539] where the question was asked only
with respect to choice functions. Here we define a subclass of the class of
tame trees (trees with a definable choice function) and prove that this is
exactly the class (actually set) of trees with definable Skolem functions.
