Rabin's uniformization problem
Yuri G. Gurevich, Saharon Shelah · Journal of Symbolic Logic · 1983
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 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 y ∈ X that satisfies ϕ*(X, y) in T.