Journal of Symbolic Logic 52 (1):219-226 (1987)

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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DOI 10.2307/2273878
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On the Bounded Monadic Theory of Well-Ordered Structures.Wolfgang Thomas - 1980 - Journal of Symbolic Logic 45 (2):334-338.
Logical Complexity of Some Classes of Tree Languages Generated by Multiple-Tree-Automata.Wojciech Buszkowski - 1980 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 26 (1-6):41-49.
Restricted Set-Theoretical Definitions in Arithmetic.Raphael M. Robinson - 1966 - Journal of Symbolic Logic 31 (4):659-660.

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