### Uniformization and Skolem Functions in the Class of Trees

by Lifsches and Shelah. [LeSh:573]

J Symbolic Logic, 1998

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.

Back to the list of publications