Journal of Symbolic Logic

Uniformization and Skolem Functions in the Class of Trees

Shmuel Lifsches and Saharon Shelah

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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 [6] where the question was asked only with respect to choice functions. A natural subclass is defined and proved to be the class of trees with definable Skolem functions. Along the way we investigate the spectrum of definable well orderings of well ordered chains.

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J. Symbolic Logic, Volume 63, Issue 1 (1998), 103-127.

First available in Project Euclid: 6 July 2007

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Lifsches, Shmuel; Shelah, Saharon. Uniformization and Skolem Functions in the Class of Trees. J. Symbolic Logic 63 (1998), no. 1, 103--127.

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