# 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}
}```
• M. Rabin
• Published 1 September 1968
• Mathematics
• Bulletin of the American Mathematical Society
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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