@article{10.2307/2273673,
    Abstract = {The set of all words in the alphabet {l, r} forms the full binary tree T. If x ∈ 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 φ<sup>*</sup>(X, y) such that for every nonempty subset X of T there is a unique y ∈ X that satisfies φ<sup>*</sup>(X, y) in T.},
    Author = {Gurevich, Yuri and Shelah, Saharon},
    File = {47 (0) (0) - a - a - m.pdf},
    ISSN = {00224812},
    Journal = {The Journal of Symbolic Logic},
    Number = {4},
    Pages = {1105--1119},
    Publisher = {Association for Symbolic Logic},
    Title = {Rabin's Uniformization Problem},
    URL = {http://www.jstor.org/stable/2273673},
    Volume = {48},
    Year = {1983},
    bdsk-url-1 = {http://www.jstor.org/stable/2273673},
    date-added = {2019-02-28 09:27:39 +0100},
    date-modified = {2019-02-28 09:27:39 +0100},
    doi = {10.2307/2273673}
}

@article{10.2307/2273673, Abstract = {The set of all words in the alphabet {l, r} forms the full binary tree T. If x ∈ 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 φ(X, y) such that for every nonempty subset X of T there is a unique y ∈ X that satisfies φ(X, y) in T.}, Author = {Gurevich, Yuri and Shelah, Saharon}, File = {47 (0) (0) - a - a - m.pdf}, ISSN = {00224812}, Journal = {The Journal of Symbolic Logic}, Number = {4}, Pages = {1105--1119}, Publisher = {Association for Symbolic Logic}, Title = {Rabin's Uniformization Problem}, URL = {http://www.jstor.org/stable/2273673}, Volume = {48}, Year = {1983}, bdsk-url-1 = {http://www.jstor.org/stable/2273673}, date-added = {2019-02-28 09:27:39 +0100}, date-modified = {2019-02-28 09:27:39 +0100}, doi = {10.2307/2273673} }