Journal of Symbolic Logic

Rabin's Uniformization Problem

Yuri Gurevich and Saharon Shelah

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The set of all words in the alphabet $\{l, r\}$ forms the full binary tree $T$. If $x \in T$ then $xl$ and $xr$ are the left and the right successors of $x$ respectively. We consider the monadic second-order language of the full binary tree with the two successor relations. This language allows quantification over elements of $T$ and over arbitrary subsets of $T$. We prove that there is no monadic second-order formula $\phi^\ast(X, y)$ such that for every nonempty subset $X$ of $T$ there is a unique $y \in X$ that satisfies $\phi^\ast(X, y)$ in $T$.

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J. Symbolic Logic, Volume 48, Issue 4 (1983), 1105-1119.

First available in Project Euclid: 6 July 2007

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Gurevich, Yuri; Shelah, Saharon. Rabin's Uniformization Problem. J. Symbolic Logic 48 (1983), no. 4, 1105--1119.

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