树类中的一致化、选择函数与井序
Uniformization, choice functions and well orders in the class of trees
摘要：
树的一元二阶理论允许对元素和任意子集进行量化。我们分类类的树的问题：一棵树T有一个可定义的选择函数（由一个一元公式参数）？一个自然的二分法出现在第一类的树没有一个可定义的选择函数和第二类的树甚至有一个可定义的良好排序的元素。这与均匀化问题有着密切的联系。
英文摘要：
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.
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