Journal of Symbolic Logic

Uniformization, Choice Functions and Well Orders in the Class of Trees

Shmuel Lifsches and Saharon Shelah

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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.

Article information

Source
J. Symbolic Logic, Volume 61, Issue 4 (1996), 1206-1227.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745131

Mathematical Reviews number (MathSciNet)
MR1456103

Zentralblatt MATH identifier
0872.03005

JSTOR
links.jstor.org

Citation

Lifsches, Shmuel; Shelah, Saharon. Uniformization, Choice Functions and Well Orders in the Class of Trees. J. Symbolic Logic 61 (1996), no. 4, 1206--1227. https://projecteuclid.org/euclid.jsl/1183745131


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