Uniformization and Skolem functions in the class of trees

Shmuel Lifsches; Saharon Shelah

doi:10.2307/2586591

Uniformization and Skolem functions in the class of trees

Shmuel Lifsches^*, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

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 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.

Original language	English
Pages (from-to)	103-127
Number of pages	25
Journal	Journal of Symbolic Logic
Volume	63
Issue number	1
DOIs	https://doi.org/10.2307/2586591
State	Published - Mar 1998

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Uniformization and Skolem functions in the class of trees

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