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Rabin's uniformization problem1

  • Yuri Gurevich (a1) and Saharon Shelah (a2)


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.


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2Department of Computer and Communication Sciences, University of Michigan, Ann Arbor, MI 48109, USA


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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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Rabin's uniformization problem1

  • Yuri Gurevich (a1) and Saharon Shelah (a2)


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