# Sh:573

• Lifsches, S., & Shelah, S. (1998). Uniformization and Skolem functions in the class of trees. J. Symbolic Logic, 63(1), 103–127.
• 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.
• Version 1994-12-13_10 (20p) published version (25p)
Bib entry
@article{Sh:573,
author = {Lifsches, Shmuel and Shelah, Saharon},
title = {{Uniformization and Skolem functions in the class of trees}},
journal = {J. Symbolic Logic},
fjournal = {The Journal of Symbolic Logic},
volume = {63},
number = {1},
year = {1998},
pages = {103--127},
issn = {0022-4812},
mrnumber = {1610786},
mrclass = {03C85},
doi = {10.2307/2586591},
note = {\href{https://arxiv.org/abs/math/9412231}{arXiv: math/9412231}},
arxiv_number = {math/9412231}
}