Uniformization and Skolem functions in the class of trees

Details Uniformization and Skolem functions in the class of trees Uniformization and Skolem functions in the class of trees

1994-12-15

arxiv.org/abs/math/9412231v1

J. Symbolic Logic 63 (1998), 103--127

Mathematics

Logic

Scientific paper

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.

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