# Decidability of second-order theories and automata on infinite trees

@article{Rabin1968DecidabilityOS, title={Decidability of second-order theories and automata on infinite trees}, author={Michael O. Rabin}, journal={Bulletin of the American Mathematical Society}, year={1968}, volume={74}, pages={1025-1029} }

Introduction. In this paper we solve the decision problem of a certain secondorder mathematical theory and apply it to obtain a large number of decidability results. The method of solution involves the development of a theory of automata on infinite trees—a chapter in combinatorial mathematics which may be of independent interest. Let £ = {0, 1}, and denote by T the set of all words (finite sequences) on 2. Let r0: T^-T and rx: T—>■ T be, respectively, the successor functions ro(x)=x0 and r1(x…

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