Abstract
Expansions of the natural number ordering by unary predicates are studied, using logics which in expressive power are located between first-order and monadic second-order logic. Building on the model-theoretic composition method of Shelah, we give two characterizations of the decidable theories of this form, in terms of effectiveness conditions on two types of “homogeneous sets”. We discuss the significance of these characterizations, show that the first-order theory of successor with extra predicates is not covered by this approach, and indicate how analogous results are obtained in the semigroup theoretic and the automata theoretic framework.
This paper was written during a visit of the first author in Aachen in March 2006, funded by the European Science Foundation ESF in the Research Networking Programme AutoMathA (Automata: From Mathematics to Applications).
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Rabinovich, A., Thomas, W. (2006). Decidable Theories of the Ordering of Natural Numbers with Unary Predicates. In: Ésik, Z. (eds) Computer Science Logic. CSL 2006. Lecture Notes in Computer Science, vol 4207. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11874683_37
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DOI: https://doi.org/10.1007/11874683_37
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