Monadic second order definable relations on the binary tree

Journal of Symbolic Logic 52 (1):219-226 (1987)
Abstract
Let S2S [WS2S] espectively be the storn [weak] monadic second order theory of the binary tree T in the language of two successor functions. An S2S-formula whose free variables are just individual variables defines a relation on T (rather than on the power set of T). We show that S2S and WS2S define the same relations on T, and we give a simple characterization of these relations
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