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)

@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}
}