Sh:539

• Lifsches, S., & Shelah, S. (1996). Uniformization, choice functions and well orders in the class of trees. J. Symbolic Logic, 61(4), 1206–1227. arXiv: math/9404227 DOI: 10.2307/2275812 MR: 1456103
• 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.
• Version 1994-04-20_10 (18p) published version (23p)

@article{Sh:539,
 author = {Lifsches, Shmuel and Shelah, Saharon},
 title = {{Uniformization, choice functions and well orders in the class of trees}},
 journal = {J. Symbolic Logic},
 fjournal = {The Journal of Symbolic Logic},
 volume = {61},
 number = {4},
 year = {1996},
 pages = {1206--1227},
 issn = {0022-4812},
 mrnumber = {1456103},
 mrclass = {03C85 (03B15)},
 doi = {10.2307/2275812},
 note = {\href{https://arxiv.org/abs/math/9404227}{arXiv: math/9404227}},
 arxiv_number = {math/9404227}
}