# Sh:573

- Lifsches, S., & Shelah, S. (1998).
*Uniformization and Skolem functions in the class of trees*. J. Symbolic Logic,**63**(1), 103–127. arXiv: math/9412231 DOI: 10.2307/2586591 MR: 1610786 -
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} }