The sentences in the examples in Section II. 1 all define regular languages. This is no accident. If we restrict the available numerical predicates appropriately, then the language defined by a monadic second-order sentence is a regular language. Moreover, as we will prove in Theorem III. 1.1 below, every regular language can be defined in this fashion. We will thus obtain a characterization of the regular languages in terms of logic.
KeywordsRegular Language Finite Automaton Order Type Numerical Relation Peano Arithmetic
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