Uniformization and Skolem functions in the class of trees
Logic
2008-02-03 v1
Abstract
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.
Cite
@article{arxiv.math/9412231,
title = {Uniformization and Skolem functions in the class of trees},
author = {Shmuel Lifsches and Saharon Shelah},
journal= {arXiv preprint arXiv:math/9412231},
year = {2008}
}