Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 61, Issue 4 (1996), 1206-1227.
Uniformization, Choice Functions and Well Orders in the Class of Trees
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.
J. Symbolic Logic, Volume 61, Issue 4 (1996), 1206-1227.
First available in Project Euclid: 6 July 2007
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Lifsches, Shmuel; Shelah, Saharon. Uniformization, Choice Functions and Well Orders in the Class of Trees. J. Symbolic Logic 61 (1996), no. 4, 1206--1227. https://projecteuclid.org/euclid.jsl/1183745131