## Journal of Symbolic Logic

### Rabin's Uniformization Problem

#### Abstract

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 $T$.

#### Article information

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

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183741418

Mathematical Reviews number (MathSciNet)
MR727798

Zentralblatt MATH identifier
0537.03007

JSTOR