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Trans. Am. Math. Soc.
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Decidability of second-order theories and automata on infinite trees

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In this paper we solve the decision problem of a certain second- order 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.

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Trans. Am. Math. Soc.

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