Uniformization, Choice Functions and Well Orders in the Class of Trees
نویسندگان
چکیده
Uniformization, choice functions and well orders in the class of trees. 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.
منابع مشابه
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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...
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عنوان ژورنال:
- J. Symb. Log.
دوره 61 شماره
صفحات -
تاریخ انتشار 1996