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Rabin's uniformization problem1

Published online by Cambridge University Press:  12 March 2014

Yuri Gurevich*
University of Michigan, Ann Arbor, Michigan 48109
Saharon Shelah
Hebrew University, Jerusalem, Israel
2Department of Computer and Communication Sciences, University of Michigan, Ann Arbor, MI 48109, USA


The set of all words in the alphabet {l, r} forms the full binary tree T. If xT 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 rand over arbitrary subsets of T. We prove that there is no monadic second-order formula ϕ*(X, y) such that for every nonempty subset X of T there is a unique yX that satisfies ϕ*(X, y) in T.

Research Article
Copyright © Association for Symbolic Logic 1983

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The work was done in principal during the 1980–81 academic year when both authors were fellows in the Institute for Advanced Studies of the Hebrew University in Jerusalem.



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