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Uniformization and skolem functions in the class of trees

Published online by Cambridge University Press:  12 March 2014

Shmuel Lifsches
Institute of Mathematics, The Hebrew University, Jerusalem, Israel, E-mail:
Saharon Shelah
Institute of Mathematics, The Hebrew University, Jerusalem, Israel, E-mail:


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.

Research Article
Copyright © Association for Symbolic Logic 1998

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