Uniformization, choice functions and well orders in the class of trees
Logic
2009-09-25 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 a definable choice function (by a monadic formula with parameters)? A natural dichotomy arises where the trees that fall in the first class don't have a definable choice function and the trees in the second class have even a definable well ordering of their elements. This has a close connection to the uniformization problem.
Keywords
Cite
@article{arxiv.math/9404227,
title = {Uniformization, choice functions and well orders in the class of trees},
author = {Shmuel Lifsches and Saharon Shelah},
journal= {arXiv preprint arXiv:math/9404227},
year = {2009}
}